Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
650 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 650 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. #20245749 | C2 | semidirect |
| 3. #20244307 | C2 | semidirect |
| 4. #20241897 | C2 | semidirect |
| 5. #20241282 | C2 | semidirect |
| 6. #20241243 | C2 | semidirect |
| 7. C47×#1490 | C2 | semidirect |
| 11. #15689413 | C4 | semidirect |
| 12. #15689318 | C4 | semidirect |
| 32. #13094024 | C2×C4 | semidirect |
| 33. #13094021 | C2×C4 | semidirect |
| 46. C4⋊(C47⋊C8) | C2×C4 | semidirect |
| 129. D4×C47 | #104 | semidirect |
| 194. #1490 | D47 | semidirect |
| 225. C47 | #9325 | semidirect |
| 332. D4 | #13093950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253479 | 2 |
| #20245749 | 2 |
| #20244307 | 2 |
| #20241897 | 2 |
| #20241282 | 2 |
| #20241243 | 2 |
| C47×#1490 | 2 |
| #9325 | 47 |