Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
414 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. C2×#10597392 | C2 | semidirect |
| 3. #11926883 | C2 | semidirect |
| 4. #11926877 | C2 | semidirect |
| 5. #11926863 | C2 | semidirect |
| 6. #11926799 | C2 | semidirect |
| 7. #11926793 | C2 | semidirect |
| 8. #11926705 | C2 | semidirect |
| 9. #11926683 | C2 | semidirect |
| 10. #11926506 | C2 | semidirect |
| 11. C19×#451 | C2 | semidirect |
| 15. C2×Q16×C19 | C22 | semidirect |
| 22. C2×#64527 | C22 | semidirect |
| 34. C19×#103 | C22 | semidirect |
| 36. #10597292 | C22 | semidirect |
| 37. #10597292 | C22 | semidirect |
| 39. #10597278 | C22 | semidirect |
| 41. #10597274 | C22 | semidirect |
| 42. #10597264 | C22 | semidirect |
| 151. #451 | D19 | semidirect |
| 164. C2×Q16 | C2×D19 | semidirect |
| 187. #103 | C2×D19 | semidirect |
| 192. C19 | #3196 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927057 | 2 |
| C2×#10597392 | 2 |
| #11926883 | 2 |
| #11926877 | 2 |
| #11926863 | 2 |
| #11926799 | 2 |
| #11926793 | 2 |
| #11926705 | 2 |
| #11926683 | 2 |
| #11926506 | 2 |
| C19×#451 | 2 |
| #3196 | 19 |