Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
386 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 2. C4×#13093959 | C2 | semidirect |
| 3. #20242146 | C2 | semidirect |
| 6. #20241279 | C2 | semidirect |
| 7. C47×#1299 | C2 | semidirect |
| 176. #1299 | D47 | semidirect |
| 205. C47 | #8673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252349 | 2 |
| C4×#13093959 | 2 |
| #20242146 | 2 |
| #20241828 | 2 |
| #20241825 | 2 |
| #20241279 | 2 |
| C47×#1299 | 2 |
| #8673 | 47 |