Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
516 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 2. #20251976 | C2 | semidirect |
| 3. #20245124 | C2 | semidirect |
| 4. C2×#15688904 | C2 | semidirect |
| 5. #20241490 | C2 | semidirect |
| 6. #20241489 | C2 | semidirect |
| 7. C47×#2145 | C2 | semidirect |
| 12. #15689378 | C4 | semidirect |
| 13. #15689373 | C4 | semidirect |
| 54. #13093956 | C2×C4 | semidirect |
| 55. #13093956 | D4 | semidirect |
| 64. C2×Q16×C47 | C2×C4 | semidirect |
| 66. C2×D8×C47 | C2×C4 | semidirect |
| 73. #106×C47 | D4 | semidirect |
| 190. #2145 | D47 | semidirect |
| 219. C47 | #13008 | semidirect |
| 226. C2×Q16 | C4×D47 | semidirect |
| 228. C2×D8 | C4×D47 | semidirect |
| 264. #106 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252993 | 2 |
| #20251976 | 2 |
| #20245124 | 2 |
| C2×#15688904 | 2 |
| #20241490 | 2 |
| #20241489 | 2 |
| C47×#2145 | 2 |
| #13008 | 47 |