Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
1260 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 485 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D19 |
| commutator, cosocle | C22×C19 | C25 |
| Frattini | C22 | C24×D19 |
| Fitting | C2×C19×#125 | C2 |
| socle | C23×C19 | C24 |
| hypercenter | C2×#125 | D19 |
| hypocenter | C19 | C2×#540 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ C2×#125 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11927150 | C2 | direct (N × H) |
| 2. C2×#10597320 | C2 | semidirect |
| 3. C2×#10597340 | C2 | semidirect |
| 4. C2×#10597341 | C2 | semidirect |
| 5. C2×#10597341 | C2 | semidirect |
| 6. C2×#10597339 | C2 | semidirect |
| 7. C2×#10597318 | C2 | semidirect |
| 8. C2×C19×#125 | C2 | semidirect |
| 14. C19×#125 | C22 | semidirect |
| 23. #10597341 | C22 | semidirect |
| 24. #10597341 | C22 | semidirect |
| 25. #10597340 | C22 | semidirect |
| 26. #10597339 | C22 | semidirect |
| 27. #10597320 | C22 | semidirect |
| 28. #10597318 | C22 | semidirect |
| 95. C2×#125 | D19 | semidirect |
| 101. C2×C19 | #540 | semidirect |
| 112. #125 | C2×D19 | semidirect |
| 126. C19 | C2×#540 | semidirect |
| 192. C2 | #11927150 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927150 | 2 |
| C2×#10597320 | 2 |
| C2×#10597340 | 2 |
| C2×#10597341 | 2 |
| C2×#10597339 | 2 |
| C2×#10597318 | 2 |
| C2×C19×#125 | 2 |
| C2×#540 | 19 |