Finite Group DatabasebetaFinite Group DatabasebetaOrder 14912.
238 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 97 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 | C4×D4×C233 | C2 |
| hypercenter | C4×D4 | D233 |
| hypocenter | C233 | #553 |
| LCS | G ▷ C22×C233 ▷ C233 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21418529 | C2 | semidirect |
| 2. #21418528 | C2 | semidirect |
| 3. #21418525 | C2 | semidirect |
| 4. #21418520 | C2 | semidirect |
| 5. #21418518 | C2 | semidirect |
| 6. #21418509 | C2 | semidirect |
| 7. #21418508 | C2 | semidirect |
| 8. #21418507 | C2 | semidirect |
| 9. #21418507 | C2 | semidirect |
| 10. C4×C22⋊D233 | C2 | semidirect |
| 11. #21418495 | C2 | semidirect |
| 12. #21418495 | C2 | semidirect |
| 13. #21418492 | C2 | semidirect |
| 14. C2×#16836573 | C2 | semidirect |
| 15. C4×D4×C233 | C2 | semidirect |
| 109. C233 | #553 | semidirect |
| 123. C4×D4 | D233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21418529 | 2 |
| #21418528 | 2 |
| #21418525 | 2 |
| #21418520 | 2 |
| #21418518 | 2 |
| #21418509 | 2 |
| #21418508 | 2 |
| #21418507 | 2 |
| C4×C22⋊D233 | 2 |
| #21418495 | 2 |
| #21418492 | 2 |
| C2×#16836573 | 2 |
| C4×D4×C233 | 2 |
| #553 | 233 |