Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
332 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 3. #20241563 | C2 | semidirect |
| 4. #20241548 | C2 | semidirect |
| 12. C47×#541 | C4 | semidirect |
| 15. C47×#492 | C4 | semidirect |
| 16. C47×#490 | C4 | semidirect |
| 22. C47×#433 | C4 | semidirect |
| 35. C4⋊Q8×C47 | C2×C4 | semidirect |
| 40. #125×C47 | C2×C4 | semidirect |
| 54. #97×C47 | C2×C4 | semidirect |
| 55. C4×C8×C47 | C2×C4 | semidirect |
| 158. #541 | Dic47 | semidirect |
| 161. #492 | Dic47 | semidirect |
| 162. #490 | Dic47 | semidirect |
| 168. #433 | Dic47 | semidirect |
| 175. C47 | #13607 | semidirect |
| 183. C4⋊Q8 | C2×Dic47 | semidirect |
| 188. #125 | C2×Dic47 | semidirect |
| 207. #97 | C2×Dic47 | semidirect |
| 208. C4×C8 | C2×Dic47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245080 | 2 |
| #20245057 | 2 |
| #20241563 | 2 |
| #20241548 | 2 |
| C47×#3222 | 2 |
| #13607 | 47 |