Finite Group DatabasebetaFinite Group DatabasebetaOrder 14912.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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 | #126×C233 | C2 |
| prime radical | C2×C22⋊D233 | C22 |
| hypercenter | #126 | D233 |
| hypocenter | C233 | #563 |
| LCS | G ▷ C22×C233 ▷ C233 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #21418535 | C2 | semidirect |
| 2. #21418534 | C2 | semidirect |
| 3. #21418530 | C2 | semidirect |
| 4. #21418529 | C2 | semidirect |
| 5. #21418528 | C2 | semidirect |
| 6. #21418526 | C2 | semidirect |
| 7. #21418525 | C2 | semidirect |
| 11. #21418515 | C2 | semidirect |
| 12. #21418513 | C2 | semidirect |
| 13. #21418512 | C2 | semidirect |
| 14. #21418512 | C2 | semidirect |
| 15. #126×C233 | C2 | semidirect |
| 97. C233 | #563 | semidirect |
| 104. #126 | D233 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21418535 | 2 |
| #21418534 | 2 |
| #21418530 | 2 |
| #21418529 | 2 |
| #21418528 | 2 |
| #21418526 | 2 |
| #21418525 | 2 |
| #21418521 | 2 |
| #21418519 | 2 |
| #21418517 | 2 |
| #21418515 | 2 |
| #21418513 | 2 |
| #21418512 | 2 |
| #126×C233 | 2 |
| #563 | 233 |