Finite Group DatabasebetaFinite Group DatabasebetaOrder 12032.
332 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. #20244136 | C2 | semidirect |
| 5. #20241484 | C2 | semidirect |
| 6. #20241482 | C2 | semidirect |
| 7. C2×C4×C16×C47 | C2 | semidirect |
| 16. #15688928 | C4 | semidirect |
| 17. #15688925 | C4 | semidirect |
| 135. C2×C4×C16 | D47 | semidirect |
| 160. C47 | #13151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15688931 | 2 |
| #20245096 | 2 |
| #20244276 | 2 |
| #20244136 | 2 |
| #20241484 | 2 |
| #20241482 | 2 |
| C2×C4×C16×C47 | 2 |
| #13151 | 47 |