Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
738 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 198 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20299677 | C2 | semidirect |
| 2. #41×#90673 | C2 | semidirect |
| 3. #20299596 | C2 | semidirect |
| 4. #20299595 | C2 | semidirect |
| 5. D113⋊#104 | C2 | semidirect |
| 6. C2×#16813686 | C2 | semidirect |
| 10. C2×#14268657 | C22 | semidirect |
| 11. D113⋊M16 | C22 | semidirect |
| 14. #16813701 | C22 | semidirect |
| 15. C2×C4×#90673 | C22 | semidirect |
| 16. #16813687 | C22 | semidirect |
| 17. #16813687 | C22 | semidirect |
| 18. #16813686 | C22 | semidirect |
| 19. #16813686 | C22 | semidirect |
| 20. #16813686 | C22 | semidirect |
| 22. #16813669 | C4 | semidirect |
| 23. #16813669 | C4 | semidirect |
| 25. #16813667 | C4 | semidirect |
| 31. H(5,𝔽2)×C113 | C4 | semidirect |
| 49. #14268647 | C2×C4 | semidirect |
| 56. #14268646 | C2×C4 | semidirect |
| 60. C2×Dic226 | C2×C4 | semidirect |
| 62. Q8×D113 | C2×C4 | semidirect |
| 68. D4×D113 | C2×C4 | semidirect |
| 75. #41×C113 | C2×C4 | semidirect |
| 77. C2×D4×C113 | C2×C4 | semidirect |
| 140. C113 | #2901 | semidirect |
| 153. H(5,𝔽2) | #90673 | semidirect |
| 189. #41 | C2×#90673 | semidirect |
| 202. C2×D4 | C2×#90673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20299677 | 2 |
| #41×#90673 | 2 |
| #20299596 | 2 |
| #20299595 | 2 |
| D113⋊#104 | 2 |
| C2×#16813686 | 2 |
| #20299433 | 2 |
| #2901 | 113 |