Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
396 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 91 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. #20243434 | C2 | semidirect |
| 3. #20241374 | C2 | semidirect |
| 4. C47×#2115 | C2 | semidirect |
| 5. C22×D376 | C4 | semidirect |
| 7. #15689376 | C4 | semidirect |
| 12. #15689161 | C4 | semidirect |
| 15. #15688880 | C22 | semidirect |
| 19. C47×#349 | C22 | semidirect |
| 146. #2115 | D47 | semidirect |
| 168. #349 | C2×D47 | semidirect |
| 170. C47 | #11868 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20253036 | 2 |
| #20243434 | 2 |
| #20241374 | 2 |
| C47×#2115 | 2 |
| #11868 | 47 |