Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
368 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20245640 | C2 | semidirect |
| 2. #20245438 | C2 | semidirect |
| 4. #20241437 | C2 | semidirect |
| 5. #20241352 | C2 | semidirect |
| 101. D4×C47 | Q32 | semidirect |
| 163. C47 | #12322 | semidirect |
| 242. D4 | #13093970 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245640 | 2 |
| #20245438 | 2 |
| #20242753 | 2 |
| #20241437 | 2 |
| #20241352 | 2 |
| D4⋊(C47⋊C16) | 2 |
| D4×Q16×C47 | 2 |
| #12322 | 47 |