Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
292 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 90 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. C2×#17984155 | C2 | semidirect |
| 4. C2×C4×#11764047 | C2 | semidirect |
| 5. #22578269 | C2 | semidirect |
| 6. #22578269 | C2 | semidirect |
| 46. #14555487 | C8 | semidirect |
| 122. C137 | #1923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984155 | 2 |
| C2×#17984145 | 2 |
| C2×C4×#11764047 | 2 |
| #22578269 | 2 |
| #22577250 | 2 |
| #1923 | 137 |