Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
496 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 3. #20245108 | C2 | semidirect |
| 4. #20244304 | C2 | semidirect |
| 5. #20241484 | C2 | semidirect |
| 6. #20241476 | C2 | semidirect |
| 24. C2×SD32×C47 | C4 | semidirect |
| 52. C2×Q16×C47 | C2×C4 | semidirect |
| 63. C2×C16×C47 | C2×C4 | semidirect |
| 173. C2×SD32 | Dic47 | semidirect |
| 186. C47 | #13019 | semidirect |
| 194. C2×Q16 | C2×Dic47 | semidirect |
| 215. C2×C16 | C2×Dic47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252240 | 2 |
| C2×#15688936 | 2 |
| #20245108 | 2 |
| #20244304 | 2 |
| #20241484 | 2 |
| #20241476 | 2 |
| C22×SD32×C47 | 2 |
| #13019 | 47 |