Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
506 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 506 conjugacy classes of subgroups — too many to draw. Only its 167 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. #20256394 | C2 | semidirect |
| 2. #20245617 | C2 | semidirect |
| 3. #20245527 | C2 | semidirect |
| 5. Q8×C47⋊C16 | C2 | semidirect |
| 73. Q8×C47 | SD32 | semidirect |
| 127. C47 | #33926 | semidirect |
| 179. Q8 | #13093968 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256394 | 2 |
| #20245617 | 2 |
| #20245527 | 2 |
| #20245433 | 2 |
| Q8×C47⋊C16 | 2 |
| C4×#13093968 | 2 |
| Q8×D8×C47 | 2 |
| #33926 | 47 |