Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
460 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×Q16×D97 | C2 | semidirect |
| 4. #20260994 | C2 | semidirect |
| 5. #20260993 | C2 | semidirect |
| 6. #20260990 | C2 | semidirect |
| 7. #20260975 | C2 | semidirect |
| 8. #20260974 | C2 | semidirect |
| 9. #20260770 | C2 | semidirect |
| 10. #20260742 | C2 | semidirect |
| 11. #470×C97 | C2 | semidirect |
| 134. C97 | #3059 | semidirect |
| 141. #470 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D97 | 2 |
| C2×#15690818 | 2 |
| #20261308 | 2 |
| #20260994 | 2 |
| #20260993 | 2 |
| #20260990 | 2 |
| #20260975 | 2 |
| #20260974 | 2 |
| #20260770 | 2 |
| #20260742 | 2 |
| #470×C97 | 2 |
| #3059 | 97 |