Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
256 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 15. #97×C97 | C4 | semidirect |
| 45. C8×C97 | C4⋊C4 | semidirect |
| 63. C97 | #1847 | semidirect |
| 77. #97 | Dic97 | semidirect |
| 108. C8 | C4⋊Dic97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690744 | 2 |
| C2×#15690742 | 2 |
| #20260605 | 2 |
| #20260601 | 2 |
| C2×#97×C97 | 2 |
| #1847 | 97 |