Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
394 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 4. #20244176 | C2 | semidirect |
| 5. #20241486 | C2 | semidirect |
| 6. #20241473 | C2 | semidirect |
| 7. C2×C47×#365 | C2 | semidirect |
| 20. #15688931 | C4 | semidirect |
| 46. #13093960 | C2×C4 | semidirect |
| 57. C2×C16×C47 | C2×C4 | semidirect |
| 148. C2×#365 | D47 | semidirect |
| 177. C47 | #12949 | semidirect |
| 202. C2×C16 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252271 | 2 |
| #20245135 | 2 |
| #20245117 | 2 |
| #20244176 | 2 |
| #20241486 | 2 |
| #20241473 | 2 |
| C2×C47×#365 | 2 |
| #12949 | 47 |