Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
256 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 84 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. #20261595 | C2 | semidirect |
| 56. D97 | #333 | semidirect |
| 58. C97 | C2×#333 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261736 | 2 |
| #20261595 | 2 |
| C4⋊Q8×D97 | 2 |
| C2×#333 | 97 |