Finite Group DatabasebetaFinite Group DatabasebetaOrder 14464.
1492 conjugacy classes of subgroups; only the 557 normal subgroups are shown.
This group has 1492 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 | C23×Q8×C113 | C2 |
| hypercenter | C23×Q8 | D113 |
| hypocenter | C113 | #3486 |
| LCS | G ▷ C22×C113 ▷ C113 | |
| UCS | C1 ◁ C22 ◁ C23×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16813670 | C2 | semidirect |
| 2. Q8×C22⋊D113 | C2 | semidirect |
| 3. #20299259 | C2 | semidirect |
| 4. #20299172 | C2 | semidirect |
| 5. #20299109 | C2 | semidirect |
| 6. #20299076 | C2 | semidirect |
| 7. C23×Q8×C113 | C2 | semidirect |
| 9. C2×#14268648 | C22 | semidirect |
| 11. C2×Q8×D113 | C22 | semidirect |
| 12. #16813620 | C22 | semidirect |
| 13. #16813611 | C22 | semidirect |
| 16. #16813598 | C22 | semidirect |
| 19. Q8×Dic113 | C22 | semidirect |
| 44. C2×Q8×C113 | D4 | semidirect |
| 75. C22×C113 | 2−1+4 | semidirect |
| 89. C113 | #3486 | semidirect |
| 91. C23×Q8 | D113 | semidirect |
| 123. C2×Q8 | C22⋊D113 | semidirect |
| 166. C22 | #16813670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16813670 | 2 |
| Q8×C22⋊D113 | 2 |
| #20299259 | 2 |
| #20299172 | 2 |
| #20299109 | 2 |
| #20299076 | 2 |
| C23×Q8×C113 | 2 |
| #3486 | 113 |