Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
394 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×#15688947 | C2 | semidirect |
| 5. #20241488 | C2 | semidirect |
| 6. #20241474 | C2 | semidirect |
| 7. C47×#1953 | C2 | semidirect |
| 20. #15688929 | C4 | semidirect |
| 45. C2×C47⋊C16 | C2×C4 | semidirect |
| 59. #108×C47 | C2×C4 | semidirect |
| 151. #1953 | D47 | semidirect |
| 177. C47 | #12949 | semidirect |
| 207. #108 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252273 | 2 |
| C2×#15688947 | 2 |
| #20245135 | 2 |
| #20245115 | 2 |
| #20241488 | 2 |
| #20241474 | 2 |
| C47×#1953 | 2 |
| #12949 | 47 |