Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
492 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 109 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. #20251979 | C2 | semidirect |
| 3. #20245124 | C2 | semidirect |
| 4. #20245015 | C2 | semidirect |
| 5. #20241503 | C2 | semidirect |
| 6. #20241486 | C2 | semidirect |
| 7. C2×C47×#360 | C2 | semidirect |
| 12. #15689395 | C4 | semidirect |
| 13. #15689390 | C4 | semidirect |
| 53. #13093960 | C2×C4 | semidirect |
| 66. C2×Q16×C47 | C2×C4 | semidirect |
| 68. C2×D8×C47 | C2×C4 | semidirect |
| 191. C2×#360 | D47 | semidirect |
| 222. C47 | #13005 | semidirect |
| 234. C2×Q16 | C4×D47 | semidirect |
| 236. C2×D8 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253104 | 2 |
| #20251979 | 2 |
| #20245124 | 2 |
| #20245015 | 2 |
| #20241503 | 2 |
| #20241486 | 2 |
| C2×C47×#360 | 2 |
| #13005 | 47 |