Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
144 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 64 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. #22578332 | C2 | semidirect |
| 3. #22578331 | C2 | semidirect |
| 52. D137 | #368 | semidirect |
| 53. C137 | C2×#368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D137⋊#108 | 2 |
| #22578332 | 2 |
| #22578331 | 2 |
| C2×C16×D137 | 2 |
| C2×#368 | 137 |