Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
246 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 77 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. #20242211 | C2 | semidirect |
| 3. #20241354 | C2 | semidirect |
| 4. #20241308 | C2 | semidirect |
| 5. C47×#1368 | C2 | semidirect |
| 19. D752 | C8 | semidirect |
| 39. D376 | C2×C8 | semidirect |
| 42. C16×C47 | C2×C8 | semidirect |
| 68. #1368 | D47 | semidirect |
| 84. C47 | #12067 | semidirect |
| 112. C16 | C8×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245265 | 2 |
| #20242211 | 2 |
| #20241354 | 2 |
| #20241308 | 2 |
| C47×#1368 | 2 |
| #12067 | 47 |