Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
530 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 105 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. #20244209 | C2 | semidirect |
| 5. #20241270 | C2 | semidirect |
| 6. #20241269 | C2 | semidirect |
| 7. C47×#1993 | C2 | semidirect |
| 10. #15689485 | C4 | semidirect |
| 55. #13093935 | C2×C4 | semidirect |
| 65. C4⋊Q8×C47 | C2×C4 | semidirect |
| 211. #1993 | D47 | semidirect |
| 246. C47 | #8999 | semidirect |
| 257. C4⋊Q8 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689485 | 2 |
| #20246559 | 2 |
| #20244209 | 2 |
| C2×#15688862 | 2 |
| #20241270 | 2 |
| #20241269 | 2 |
| C47×#1993 | 2 |
| #8999 | 47 |