Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #11927172 | C2 | semidirect |
| 2. #11926908 | C2 | semidirect |
| 3. #11926903 | C2 | semidirect |
| 4. #11926898 | C2 | semidirect |
| 5. #11926890 | C2 | semidirect |
| 6. #11926549 | C2 | semidirect |
| 7. #11926545 | C2 | semidirect |
| 8. #11926540 | C2 | semidirect |
| 9. C2×#10597289 | C2 | semidirect |
| 10. #11926500 | C2 | semidirect |
| 27. #10597316 | C22 | semidirect |
| 28. #10597315 | C22 | semidirect |
| 29. #10597292 | C22 | semidirect |
| 30. #10597292 | C22 | semidirect |
| 31. #10597292 | C22 | semidirect |
| 36. #10597289 | C22 | semidirect |
| 37. #10597289 | C22 | semidirect |
| 38. #10597289 | C22 | semidirect |
| 39. #10597260 | C22 | semidirect |
| 40. C4×C19⋊C8 | C22 | semidirect |
| 176. C19 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11927172 | 2 |
| #11926908 | 2 |
| #11926903 | 2 |
| #11926898 | 2 |
| #11926890 | 2 |
| #11926549 | 2 |
| #11926545 | 2 |
| #11926540 | 2 |
| C2×#10597289 | 2 |
| #11926500 | 2 |
| C19×#535 | 2 |
| #3136 | 19 |