Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
240 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 75 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. #20245530 | C2 | semidirect |
| 4. #20241452 | C2 | semidirect |
| 5. #20241444 | C2 | semidirect |
| 7. C8×Q16×C47 | C2 | semidirect |
| 51. Q16×C47 | SD16 | semidirect |
| 91. C8×C47 | SD32 | semidirect |
| 110. C8×Q16 | D47 | semidirect |
| 133. C47 | #12417 | semidirect |
| 162. Q16 | #10625325 | semidirect |
| 202. C8 | #13093967 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245530 | 2 |
| #20245428 | 2 |
| #20242980 | 2 |
| #20241452 | 2 |
| #20241444 | 2 |
| #20241433 | 2 |
| C8×Q16×C47 | 2 |
| #12417 | 47 |