Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
292 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 11. #17984087 | C4 | semidirect |
| 35. C4⋊Dic137 | Q8 | semidirect |
| 49. C4⋊C4×C137 | Q8 | semidirect |
| 102. C137 | #1987 | semidirect |
| 149. C4⋊C4 | Dic274 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984087 | 2 |
| C2×#17984017 | 2 |
| C4⋊C4×Dic137 | 2 |
| #22577166 | 2 |
| #22577165 | 2 |
| #340×C137 | 2 |
| #1987 | 137 |