Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
252 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 71 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. D4×C47⋊C16 | C2 | semidirect |
| 4. #20241461 | C2 | semidirect |
| 5. #20241437 | C2 | semidirect |
| 6. #20241433 | C2 | semidirect |
| 7. C47×#1669 | C2 | semidirect |
| 73. C47⋊C16 | D8 | semidirect |
| 79. D4×C47 | SD32 | semidirect |
| 115. #1669 | D47 | semidirect |
| 140. C47 | #12432 | semidirect |
| 202. D4 | #13093967 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245645 | 2 |
| D4×C47⋊C16 | 2 |
| #20242743 | 2 |
| #20241461 | 2 |
| #20241437 | 2 |
| #20241433 | 2 |
| C47×#1669 | 2 |
| #12432 | 47 |