Finite Group DatabasebetaFinite Group DatabasebetaOrder 2432.
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#10597355 | C2 | semidirect |
| 2. C2×#10597354 | C2 | semidirect |
| 3. C2×#10597350 | C2 | semidirect |
| 4. C22×#64516 | C2 | semidirect |
| 5. #11927120 | C2 | semidirect |
| 6. #11927113 | C2 | semidirect |
| 7. #11926938 | C2 | semidirect |
| 8. #11926933 | C2 | semidirect |
| 9. #11926928 | C2 | semidirect |
| 10. #11926917 | C2 | semidirect |
| 11. C19×#405 | C2 | semidirect |
| 21. C2×Dic76 | C22 | semidirect |
| 22. C2×Dic76 | C22 | semidirect |
| 25. C2×D152 | C22 | semidirect |
| 30. C2×#64516 | C22 | semidirect |
| 31. C2×#64516 | C22 | semidirect |
| 32. C2×#64516 | C22 | semidirect |
| 38. #10597321 | C22 | semidirect |
| 40. #10597315 | C22 | semidirect |
| 41. C19×#97 | C22 | semidirect |
| 42. C4×C8×C19 | C22 | semidirect |
| 67. M16×C19 | D4 | semidirect |
| 68. C2×C8×C19 | D4 | semidirect |
| 153. #405 | D19 | semidirect |
| 189. #97 | C2×D19 | semidirect |
| 190. C4×C8 | C2×D19 | semidirect |
| 191. C19 | #3154 | semidirect |
| 226. M16 | D76 | semidirect |
| 227. C2×C8 | D76 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10597355 | 2 |
| C2×#10597354 | 2 |
| C2×#10597350 | 2 |
| C22×#64516 | 2 |
| #11927120 | 2 |
| #11927113 | 2 |
| #11926938 | 2 |
| #11926933 | 2 |
| #11926928 | 2 |
| #11926917 | 2 |
| C19×#405 | 2 |
| #3154 | 19 |