Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
186 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 69 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. #20245269 | C2 | semidirect |
| 2. #20241592 | C2 | semidirect |
| 3. #20241572 | C2 | semidirect |
| 4. C32×Dic47 | C2 | semidirect |
| 12. C47×Q64 | C4 | semidirect |
| 13. C47×SD64 | C4 | semidirect |
| 14. C47×D32 | C4 | semidirect |
| 70. Q64 | Dic47 | semidirect |
| 71. SD64 | Dic47 | semidirect |
| 72. D32 | Dic47 | semidirect |
| 78. C47 | #13655 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245269 | 2 |
| #20241592 | 2 |
| #20241572 | 2 |
| C32×Dic47 | 2 |
| C47×#2262 | 2 |
| #13655 | 47 |