Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
252 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 252 conjugacy classes of subgroups — too many to draw. Only its 72 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. D137⋊#108 | C2 | semidirect |
| 3. #22578272 | C2 | semidirect |
| 84. C137 | #1813 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D137⋊#108 | 2 |
| #22578389 | 2 |
| #22578272 | 2 |
| C2×#17984094 | 2 |
| #1813 | 137 |