Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
364 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 91 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. #20253911 | C2 | semidirect |
| 4. #20241504 | C2 | semidirect |
| 5. #20241503 | C2 | semidirect |
| 6. #20241467 | C2 | semidirect |
| 49. C2×Q16×C47 | Q8 | semidirect |
| 51. C2×D8×C47 | Q8 | semidirect |
| 171. C47 | #13373 | semidirect |
| 177. C2×Q16 | Dic94 | semidirect |
| 179. C2×D8 | Dic94 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253911 | 2 |
| #20245124 | 2 |
| #20244282 | 2 |
| #20241504 | 2 |
| #20241503 | 2 |
| #20241467 | 2 |
| C47×#2145 | 2 |
| #13373 | 47 |