Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
360 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 360 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 |
|---|---|---|
| 1. #22578404 | C2 | semidirect |
| 2. #22578261 | C2 | semidirect |
| 5. #17984155 | C22 | semidirect |
| 68. D137 | #331 | semidirect |
| 69. C137 | C2×#331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578404 | 2 |
| #22578261 | 2 |
| #127×D137 | 2 |
| C2×#331 | 137 |