Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
632 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 107 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. #20246111 | C2 | semidirect |
| 3. #20244219 | C2 | semidirect |
| 4. #20242057 | C2 | semidirect |
| 5. #20241947 | C2 | semidirect |
| 6. #20241216 | C2 | semidirect |
| 7. C47×#1286 | C2 | semidirect |
| 11. #15689500 | C4 | semidirect |
| 12. #15689470 | C4 | semidirect |
| 33. #13094024 | C2×C4 | semidirect |
| 37. #13094021 | C2×C4 | semidirect |
| 66. C4×C8×C47 | C2×C4 | semidirect |
| 121. C4×Dic47 | D8 | semidirect |
| 210. #1286 | D47 | semidirect |
| 238. C47 | #9299 | semidirect |
| 276. C4×C8 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20254308 | 2 |
| #20246111 | 2 |
| #20244219 | 2 |
| #20242057 | 2 |
| #20241947 | 2 |
| #20241216 | 2 |
| C47×#1286 | 2 |
| #9299 | 47 |