Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
662 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 662 conjugacy classes of subgroups — too many to draw. Only its 137 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. #20252297 | C2 | semidirect |
| 2. #20252023 | C2 | semidirect |
| 3. #20244962 | C2 | semidirect |
| 4. #20244676 | C2 | semidirect |
| 6. #20244056 | C2 | semidirect |
| 7. #20243834 | C2 | semidirect |
| 8. #20243803 | C2 | semidirect |
| 9. #20243625 | C2 | semidirect |
| 10. #20243538 | C2 | semidirect |
| 11. C47×#2091 | C2 | semidirect |
| 71. #13093934 | D4 | semidirect |
| 73. C8×Dic47 | D4 | semidirect |
| 193. #2091 | D47 | semidirect |
| 233. C47 | #29385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252297 | 2 |
| #20252023 | 2 |
| #20244962 | 2 |
| #20244676 | 2 |
| #20244455 | 2 |
| #20244056 | 2 |
| #20243834 | 2 |
| #20243803 | 2 |
| #20243625 | 2 |
| #20243538 | 2 |
| C47×#2091 | 2 |
| #29385 | 47 |