Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
462 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 462 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. #20252305 | C2 | semidirect |
| 3. C2×#15688931 | C2 | semidirect |
| 4. #20244284 | C2 | semidirect |
| 5. #20241504 | C2 | semidirect |
| 6. #20241476 | C2 | semidirect |
| 7. C47×#2138 | C2 | semidirect |
| 11. #15689563 | C4 | semidirect |
| 13. #15689558 | C4 | semidirect |
| 178. #2138 | D47 | semidirect |
| 209. C47 | #13021 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256522 | 2 |
| #20252305 | 2 |
| C2×#15688931 | 2 |
| #20244284 | 2 |
| #20241504 | 2 |
| #20241476 | 2 |
| C47×#2138 | 2 |
| #13021 | 47 |