Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
578 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 578 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. #20244362 | C2 | semidirect |
| 5. #20241270 | C2 | semidirect |
| 6. #20241269 | C2 | semidirect |
| 7. C47×#1993 | C2 | semidirect |
| 12. #15689515 | C4 | semidirect |
| 57. #13093935 | C2×C4 | semidirect |
| 67. C4⋊Q8×C47 | C2×C4 | semidirect |
| 216. #1993 | D47 | semidirect |
| 250. C47 | #9003 | semidirect |
| 267. 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×#15689515 | 2 |
| #20246559 | 2 |
| #20244362 | 2 |
| C2×#15688862 | 2 |
| #20241270 | 2 |
| #20241269 | 2 |
| C47×#1993 | 2 |
| #9003 | 47 |