Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
230 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 3. #20241453 | C2 | semidirect |
| 4. #20241358 | C2 | semidirect |
| 6. #20241309 | C2 | semidirect |
| 7. C47×#1579 | C2 | semidirect |
| 26. #13093967 | C8 | semidirect |
| 48. Q16×C47 | C2×C8 | semidirect |
| 66. C47⋊C16 | C2×C8 | semidirect |
| 101. #1579 | D47 | semidirect |
| 125. C47 | #12065 | semidirect |
| 151. Q16 | C8×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20245250 | 2 |
| #20242213 | 2 |
| #20241453 | 2 |
| #20241358 | 2 |
| #20241354 | 2 |
| #20241309 | 2 |
| C47×#1579 | 2 |
| #12065 | 47 |