Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
480 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 133 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. C4⋊Q8×D97 | C2 | semidirect |
| 4. #20260945 | C2 | semidirect |
| 5. #20260943 | C2 | semidirect |
| 6. #20260941 | C2 | semidirect |
| 7. #20260939 | C2 | semidirect |
| 8. #20260937 | C2 | semidirect |
| 9. #20260757 | C2 | semidirect |
| 10. #20260742 | C2 | semidirect |
| 11. #462×C97 | C2 | semidirect |
| 132. C4×C97 | #137 | semidirect |
| 139. Dic97 | #137 | semidirect |
| 146. C97 | #3039 | semidirect |
| 152. #462 | D97 | semidirect |
| 283. C4 | #15690842 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690842 | 2 |
| C4⋊Q8×D97 | 2 |
| C4×#13095512 | 2 |
| #20260945 | 2 |
| #20260943 | 2 |
| #20260941 | 2 |
| #20260939 | 2 |
| #20260937 | 2 |
| #20260757 | 2 |
| #20260742 | 2 |
| #462×C97 | 2 |
| #3039 | 97 |