Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
568 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 1. #20256522 | C2 | semidirect |
| 2. C2×#15689558 | C2 | semidirect |
| 3. #20253874 | C2 | semidirect |
| 4. #20245123 | C2 | semidirect |
| 5. #20245103 | C2 | semidirect |
| 6. #20241474 | C2 | semidirect |
| 7. C47×#1976 | C2 | semidirect |
| 65. #13093964 | D4 | semidirect |
| 67. C2×C47⋊C16 | D4 | semidirect |
| 73. C2×Q16×C47 | D4 | semidirect |
| 75. C2×D8×C47 | D4 | semidirect |
| 216. #1976 | D47 | semidirect |
| 250. C47 | #13334 | semidirect |
| 265. C2×Q16 | D188 | semidirect |
| 277. C2×D8 | D188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20256522 | 2 |
| C2×#15689558 | 2 |
| #20253874 | 2 |
| #20245123 | 2 |
| #20245103 | 2 |
| #20241474 | 2 |
| C47×#1976 | 2 |
| #13334 | 47 |