Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
492 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #20245107 | C2 | semidirect |
| 4. C2×#15688928 | C2 | semidirect |
| 6. #20241498 | C2 | semidirect |
| 7. C47×#1382 | C2 | semidirect |
| 14. #15689399 | C4 | semidirect |
| 38. C2×Dic188 | C2×C4 | semidirect |
| 68. #108×C47 | C2×C4 | semidirect |
| 182. #1382 | D47 | semidirect |
| 209. C47 | #12997 | semidirect |
| 245. #108 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689399 | 2 |
| #20251985 | 2 |
| #20245107 | 2 |
| C2×#15688928 | 2 |
| C2×#15688906 | 2 |
| #20241498 | 2 |
| C47×#1382 | 2 |
| #12997 | 47 |