Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
146 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 61 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. #20260852 | C2 | semidirect |
| 2. #20260565 | C2 | semidirect |
| 3. #20260542 | C2 | semidirect |
| 4. C16×Dic97 | C2 | semidirect |
| 12. Q32×C97 | C4 | semidirect |
| 13. SD32×C97 | C4 | semidirect |
| 14. D16×C97 | C4 | semidirect |
| 50. C97 | #2178 | semidirect |
| 58. Q32 | Dic97 | semidirect |
| 59. SD32 | Dic97 | semidirect |
| 60. D16 | Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20260852 | 2 |
| #20260565 | 2 |
| #20260542 | 2 |
| C16×Dic97 | 2 |
| #508×C97 | 2 |
| #2178 | 97 |