Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
522 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 522 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 |
|---|---|---|
| 1. #20252189 | C2 | semidirect |
| 2. C2×#15688933 | C2 | semidirect |
| 3. #20245104 | C2 | semidirect |
| 4. #20244265 | C2 | semidirect |
| 5. #20241494 | C2 | semidirect |
| 6. #20241471 | C2 | semidirect |
| 24. C47×#509 | C4 | semidirect |
| 63. C2×D8×C47 | C2×C4 | semidirect |
| 69. M32×C47 | C2×C4 | semidirect |
| 91. Q16×C47 | C22⋊C4 | semidirect |
| 99. D8×C47 | C22⋊C4 | semidirect |
| 196. #509 | Dic47 | semidirect |
| 212. C47 | #13025 | semidirect |
| 226. C2×D8 | C2×Dic47 | semidirect |
| 244. M32 | C2×Dic47 | semidirect |
| 276. Q16 | C22⋊Dic47 | semidirect |
| 284. D8 | C22⋊Dic47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252189 | 2 |
| C2×#15688933 | 2 |
| #20245104 | 2 |
| #20244265 | 2 |
| #20241494 | 2 |
| #20241471 | 2 |
| C2×C47×#509 | 2 |
| #13025 | 47 |