Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
232 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 67 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. C2×#15688958 | C2 | semidirect |
| 2. #20245638 | C2 | semidirect |
| 3. C4⋊(C47⋊C32) | C2 | semidirect |
| 4. #20241565 | C2 | semidirect |
| 5. C4×D16×C47 | C2 | semidirect |
| 26. D16×C47 | D4 | semidirect |
| 76. C4×C47 | D32 | semidirect |
| 81. C4×D16 | D47 | semidirect |
| 99. C47 | #13685 | semidirect |
| 109. D16 | D188 | semidirect |
| 159. C4 | #15688958 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15688958 | 2 |
| #20245638 | 2 |
| C4⋊(C47⋊C32) | 2 |
| #20241565 | 2 |
| C4×D16×C47 | 2 |
| #13685 | 47 |