Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
452 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 93 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. #20242158 | C2 | semidirect |
| 3. #20242038 | C2 | semidirect |
| 4. #20241947 | C2 | semidirect |
| 5. #20241709 | C2 | semidirect |
| 6. #20241246 | C2 | semidirect |
| 7. C47×#1804 | C2 | semidirect |
| 186. #1804 | D47 | semidirect |
| 218. C47 | #10465 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20252852 | 2 |
| #20242158 | 2 |
| #20242038 | 2 |
| #20241947 | 2 |
| #20241709 | 2 |
| #20241246 | 2 |
| C47×#1804 | 2 |
| #10465 | 47 |