Finite Group DatabasebetaFinite Group DatabasebetaOrder 14912.
240 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 93 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 | C23×D233 |
| commutator, socle, cosocle | C22×C233 | C24 |
| Fitting | #123×C233 | C2 |
| hypercenter | #123 | D233 |
| hypocenter | C233 | #540 |
| LCS | G ▷ C22×C233 ▷ C233 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21418531 | C2 | semidirect |
| 2. #21418525 | C2 | semidirect |
| 3. #21418520 | C2 | semidirect |
| 4. #21418519 | C2 | semidirect |
| 5. #21418517 | C2 | semidirect |
| 6. #21418510 | C2 | semidirect |
| 7. #21418509 | C2 | semidirect |
| 8. #21418508 | C2 | semidirect |
| 9. #21418508 | C2 | semidirect |
| 10. #21418508 | C2 | semidirect |
| 11. #21418507 | C2 | semidirect |
| 12. C4×C22⋊D233 | C2 | semidirect |
| 13. #21418495 | C2 | semidirect |
| 14. #21418493 | C2 | semidirect |
| 15. #123×C233 | C2 | semidirect |
| 115. C233 | #540 | semidirect |
| 122. #123 | D233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21418531 | 2 |
| #21418525 | 2 |
| #21418520 | 2 |
| #21418519 | 2 |
| #21418517 | 2 |
| #21418510 | 2 |
| #21418509 | 2 |
| #21418508 | 2 |
| #21418507 | 2 |
| C4×C22⋊D233 | 2 |
| #21418495 | 2 |
| #21418493 | 2 |
| #123×C233 | 2 |
| #540 | 233 |