Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
1748 conjugacy classes of subgroups; only the 557 normal subgroups are shown.
This group has 1748 conjugacy classes of subgroups — too many to draw. Only its 557 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D113 |
| commutator, socle, cosocle | C22×C113 | C25 |
| Fitting | C4×#41×C113 | C2 |
| hypercenter | C4×#41 | D113 |
| hypocenter | C113 | #3498 |
| LCS | G ▷ C22×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ C4×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16813668 | C2 | semidirect |
| 2. #20299270 | C2 | semidirect |
| 3. D4×D452 | C2 | semidirect |
| 4. #20299167 | C2 | semidirect |
| 5. #20299148 | C2 | semidirect |
| 6. C2×#16813619 | C2 | semidirect |
| 7. C4×#41×C113 | C2 | semidirect |
| 9. C2×#14268648 | C22 | semidirect |
| 10. C2×#14268647 | C22 | semidirect |
| 11. C22×D452 | C22 | semidirect |
| 12. C22×D452 | C22 | semidirect |
| 13. C2×D4×D113 | C22 | semidirect |
| 14. #16813622 | C22 | semidirect |
| 15. #16813619 | C22 | semidirect |
| 16. #16813619 | C22 | semidirect |
| 17. #16813619 | C22 | semidirect |
| 18. #16813610 | C22 | semidirect |
| 19. #16813597 | C22 | semidirect |
| 20. #16813596 | C22 | semidirect |
| 21. #16813592 | C22 | semidirect |
| 22. C4×D452 | C22 | semidirect |
| 24. C4×Q8×C113 | C22 | semidirect |
| 25. C4×D4×C113 | C22 | semidirect |
| 26. #117×C113 | C22 | semidirect |
| 27. C2×C42×C113 | C22 | semidirect |
| 43. #41×C113 | D4 | semidirect |
| 57. Q8×C113 | C2×D4 | semidirect |
| 58. D4×C113 | C2×D4 | semidirect |
| 60. C2×C4×C113 | C2×D4 | semidirect |
| 82. C4×C113 | H(5,𝔽2) | semidirect |
| 89. C113 | #3498 | semidirect |
| 96. C4×#41 | D113 | semidirect |
| 112. C4×Q8 | C2×D113 | semidirect |
| 114. C4×D4 | C2×D113 | semidirect |
| 115. #117 | C2×D113 | semidirect |
| 116. C2×C42 | C2×D113 | semidirect |
| 120. #41 | D452 | semidirect |
| 147. Q8 | C2×D452 | semidirect |
| 153. D4 | C2×D452 | semidirect |
| 157. C2×C4 | C2×D452 | semidirect |
| 172. C4 | #16813668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813668 | 2 |
| #20299270 | 2 |
| D4×D452 | 2 |
| #20299167 | 2 |
| #20299148 | 2 |
| C2×#16813619 | 2 |
| C4×#41×C113 | 2 |
| #3498 | 113 |