Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
738 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 143 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. C22×Q8×D19 | C2 | semidirect |
| 2. C2×#10597364 | C2 | semidirect |
| 4. #11926699 | C2 | semidirect |
| 5. #11926698 | C2 | semidirect |
| 6. #11926685 | C2 | semidirect |
| 7. #11926684 | C2 | semidirect |
| 8. #11926683 | C2 | semidirect |
| 9. #11926551 | C2 | semidirect |
| 10. #11926506 | C2 | semidirect |
| 11. C19×#451 | C2 | semidirect |
| 23. C2×Q16×C19 | C22 | semidirect |
| 26. C2×#64528 | C22 | semidirect |
| 27. C2×#64527 | C22 | semidirect |
| 30. C2×#64516 | C22 | semidirect |
| 38. C19×#103 | C22 | semidirect |
| 40. #10597292 | C22 | semidirect |
| 43. #10597273 | C22 | semidirect |
| 44. #10597267 | C22 | semidirect |
| 61. Q8×D19 | D4 | semidirect |
| 142. C22×C19 | #137 | semidirect |
| 153. C2×D19 | #137 | semidirect |
| 168. #451 | D19 | semidirect |
| 194. C2×Q16 | C2×D19 | semidirect |
| 210. #103 | C2×D19 | semidirect |
| 214. C19 | #3004 | semidirect |
| 321. C22 | #10597364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D19 | 2 |
| C2×#10597364 | 2 |
| #11927057 | 2 |
| #11926699 | 2 |
| #11926698 | 2 |
| #11926685 | 2 |
| #11926684 | 2 |
| #11926683 | 2 |
| #11926551 | 2 |
| #11926506 | 2 |
| C19×#451 | 2 |
| #3004 | 19 |