Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 141 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11927094 | C2 | semidirect |
| 2. C2×C4×D76 | C2 | semidirect |
| 3. #11926858 | C2 | semidirect |
| 4. #11926825 | C2 | semidirect |
| 5. #11926740 | C2 | semidirect |
| 6. #11926680 | C2 | semidirect |
| 7. C4×D152 | C2 | semidirect |
| 8. C19×#431 | C2 | semidirect |
| 19. #10597320 | C22 | semidirect |
| 25. C4×D76 | C22 | semidirect |
| 26. #10597315 | C22 | semidirect |
| 27. C19×C4⋊C8 | C22 | semidirect |
| 29. C4×C8×C19 | C22 | semidirect |
| 31. #10597278 | C22 | semidirect |
| 32. #10597275 | C22 | semidirect |
| 73. C2×C4×C19 | D8 | semidirect |
| 89. D76 | #41 | semidirect |
| 122. #431 | D19 | semidirect |
| 148. C4⋊C8 | C2×D19 | semidirect |
| 152. C4×C8 | C2×D19 | semidirect |
| 153. C19 | #3100 | semidirect |
| 208. C2×C4 | D152 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927094 | 2 |
| C2×C4×D76 | 2 |
| #11926858 | 2 |
| #11926825 | 2 |
| #11926740 | 2 |
| #11926680 | 2 |
| C4×D152 | 2 |
| C19×#431 | 2 |
| #3100 | 19 |