Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
288 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 55 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. #20256526 | C2 | semidirect |
| 2. C2×#15688958 | C2 | semidirect |
| 3. #20245505 | C2 | semidirect |
| 4. #20241579 | C2 | semidirect |
| 5. #20241572 | C2 | semidirect |
| 6. #20241531 | C2 | semidirect |
| 7. C47×#2263 | C2 | semidirect |
| 17. C2×C47⋊C32 | C22 | semidirect |
| 18. #15688953 | C22 | semidirect |
| 21. C2×D16×C47 | C22 | semidirect |
| 24. C47×M64 | C22 | semidirect |
| 117. #2263 | D47 | semidirect |
| 136. C2×D16 | C2×D47 | semidirect |
| 142. M64 | C2×D47 | semidirect |
| 146. C47 | #13669 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256526 | 2 |
| C2×#15688958 | 2 |
| #20245505 | 2 |
| #20241579 | 2 |
| #20241572 | 2 |
| #20241531 | 2 |
| C47×#2263 | 2 |
| #13669 | 47 |