Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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. #20261292 | C2 | semidirect |
| 3. #20261077 | C2 | semidirect |
| 4. #20261031 | C2 | semidirect |
| 5. #20261026 | C2 | semidirect |
| 6. #20260946 | C2 | semidirect |
| 7. #20260941 | C2 | semidirect |
| 9. #20260843 | C2 | semidirect |
| 10. #20260837 | C2 | semidirect |
| 11. #432×C97 | C2 | semidirect |
| 137. C97 | #3116 | semidirect |
| 148. #432 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261292 | 2 |
| C4×#13095511 | 2 |
| #20261077 | 2 |
| #20261031 | 2 |
| #20261026 | 2 |
| #20260946 | 2 |
| #20260941 | 2 |
| #20260899 | 2 |
| #20260843 | 2 |
| #20260837 | 2 |
| #432×C97 | 2 |
| #3116 | 97 |