Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
516 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 131 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. #20251978 | C2 | semidirect |
| 2. #20245124 | C2 | semidirect |
| 3. C2×#15688905 | C2 | semidirect |
| 4. #20241489 | C2 | semidirect |
| 16. C47×#470 | C4 | semidirect |
| 17. C47×#469 | C4 | semidirect |
| 34. #13093956 | D4 | semidirect |
| 39. C2×Q16×C47 | C2×C4 | semidirect |
| 41. C2×D8×C47 | C2×C4 | semidirect |
| 55. #106×C47 | C2×C4 | semidirect |
| 172. #470 | Dic47 | semidirect |
| 173. #469 | Dic47 | semidirect |
| 182. C47 | #13008 | semidirect |
| 187. C2×Q16 | C2×Dic47 | semidirect |
| 189. C2×D8 | C2×Dic47 | semidirect |
| 217. #106 | C2×Dic47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20251978 | 2 |
| #20245124 | 2 |
| C2×#15688905 | 2 |
| #20241489 | 2 |
| C47×#3054 | 2 |
| #13008 | 47 |