Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
386 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 119 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. #20261290 | C2 | semidirect |
| 3. #20261079 | C2 | semidirect |
| 4. #20261027 | C2 | semidirect |
| 5. #20260946 | C2 | semidirect |
| 6. #20260940 | C2 | semidirect |
| 8. #20260841 | C2 | semidirect |
| 9. #20260832 | C2 | semidirect |
| 10. #20260791 | C2 | semidirect |
| 11. #476×C97 | C2 | semidirect |
| 137. C97 | #3116 | semidirect |
| 142. #476 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261290 | 2 |
| C4×#13095510 | 2 |
| #20261079 | 2 |
| #20261027 | 2 |
| #20260946 | 2 |
| #20260940 | 2 |
| #20260898 | 2 |
| #20260841 | 2 |
| #20260832 | 2 |
| #20260791 | 2 |
| #476×C97 | 2 |
| #3116 | 97 |