Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
494 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 494 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. #20252262 | C2 | semidirect |
| 3. C2×#15688931 | C2 | semidirect |
| 4. #20244299 | C2 | semidirect |
| 5. #20241496 | C2 | semidirect |
| 6. #20241476 | C2 | semidirect |
| 7. C2×C47×#357 | C2 | semidirect |
| 11. #15689559 | C4 | semidirect |
| 47. #13093964 | C2×C4 | semidirect |
| 64. C2×D8×C47 | C2×C4 | semidirect |
| 185. C2×#357 | D47 | semidirect |
| 216. C47 | #13022 | semidirect |
| 231. C2×D8 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689559 | 2 |
| #20252262 | 2 |
| C2×#15688931 | 2 |
| #20244299 | 2 |
| #20241496 | 2 |
| #20241476 | 2 |
| C2×C47×#357 | 2 |
| #13022 | 47 |