Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
384 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 384 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. #20245645 | C2 | semidirect |
| 2. #20245428 | C2 | semidirect |
| 4. #20241437 | C2 | semidirect |
| 5. #20241352 | C2 | semidirect |
| 6. D4⋊(C47⋊C16) | C2 | semidirect |
| 7. D4×Q16×C47 | C2 | semidirect |
| 72. Q16×C47 | D8 | semidirect |
| 103. D4×C47 | SD32 | semidirect |
| 141. D4×Q16 | D47 | semidirect |
| 170. C47 | #12318 | semidirect |
| 218. Q16 | #10625334 | semidirect |
| 254. D4 | #13093967 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245645 | 2 |
| #20245428 | 2 |
| #20242743 | 2 |
| #20241437 | 2 |
| #20241352 | 2 |
| D4⋊(C47⋊C16) | 2 |
| D4×Q16×C47 | 2 |
| #12318 | 47 |