Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
564 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 113 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. #20251976 | C2 | semidirect |
| 3. #20245105 | C2 | semidirect |
| 4. #20245103 | C2 | semidirect |
| 5. C2×#15688904 | C2 | semidirect |
| 6. #20241495 | C2 | semidirect |
| 7. C47×#1386 | C2 | semidirect |
| 14. #15689377 | C4 | semidirect |
| 34. C2×D376 | C2×C4 | semidirect |
| 55. #13093958 | D4 | semidirect |
| 66. #107×C47 | D4 | semidirect |
| 69. #106×C47 | C2×C4 | semidirect |
| 187. #1386 | D47 | semidirect |
| 212. C47 | #12999 | semidirect |
| 250. #107 | D188 | semidirect |
| 255. #106 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689377 | 2 |
| #20251976 | 2 |
| #20245105 | 2 |
| #20245103 | 2 |
| C2×#15688904 | 2 |
| #20241495 | 2 |
| C47×#1386 | 2 |
| #12999 | 47 |