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. #20245104 | C2 | semidirect |
| 4. C2×#15688904 | C2 | semidirect |
| 5. #20241494 | C2 | semidirect |
| 6. #20241493 | C2 | semidirect |
| 7. C47×#2140 | C2 | semidirect |
| 13. #15689373 | C4 | semidirect |
| 49. #13093958 | D4 | semidirect |
| 53. #13093956 | C2×C4 | semidirect |
| 62. C2×D8×C47 | C2×C4 | semidirect |
| 68. #107×C47 | D4 | semidirect |
| 184. #2140 | D47 | semidirect |
| 212. C47 | #12999 | semidirect |
| 221. C2×D8 | C4×D47 | semidirect |
| 250. #107 | C22⋊D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689373 | 2 |
| #20251976 | 2 |
| #20245104 | 2 |
| C2×#15688904 | 2 |
| #20241494 | 2 |
| #20241493 | 2 |
| C47×#2140 | 2 |
| #12999 | 47 |