Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
402 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 59 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. #20245324 | C2 | semidirect |
| 3. #20245307 | C2 | semidirect |
| 4. #20244509 | C2 | semidirect |
| 5. #20241407 | C2 | semidirect |
| 6. #20241404 | C2 | semidirect |
| 7. C47×#1315 | C2 | semidirect |
| 178. #1315 | D47 | semidirect |
| 204. C47 | #12113 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254290 | 2 |
| #20245324 | 2 |
| #20245307 | 2 |
| #20244509 | 2 |
| #20241407 | 2 |
| #20241404 | 2 |
| C47×#1315 | 2 |
| #12113 | 47 |