Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
538 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#15689236 | C2 | semidirect |
| 3. C2×#15688935 | C2 | semidirect |
| 4. C2×#15688933 | C2 | semidirect |
| 5. #20241488 | C2 | semidirect |
| 6. #20241468 | C2 | semidirect |
| 7. C47×#1975 | C2 | semidirect |
| 12. C2×#13093967 | C4 | semidirect |
| 13. C2×#13093965 | C4 | semidirect |
| 46. C2×C47⋊C16 | C2×C4 | semidirect |
| 55. C2×Q16×C47 | C2×C4 | semidirect |
| 57. C2×D8×C47 | C2×C4 | semidirect |
| 177. #1975 | D47 | semidirect |
| 205. C47 | #13037 | semidirect |
| 213. C2×Q16 | C4×D47 | semidirect |
| 221. C2×D8 | C4×D47 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15689558 | 2 |
| C2×#15689236 | 2 |
| C2×#15688935 | 2 |
| C2×#15688933 | 2 |
| #20241488 | 2 |
| #20241468 | 2 |
| C47×#1975 | 2 |
| #13037 | 47 |