Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
298 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 15. #17984012 | C4 | semidirect |
| 66. Q8×C137 | C4⋊C4 | semidirect |
| 109. C137 | #1863 | semidirect |
| 168. Q8 | #14555489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984021 | 2 |
| C2×#17984012 | 2 |
| #22577301 | 2 |
| #22577165 | 2 |
| #22577158 | 2 |
| C2×C4×Q8×C137 | 2 |
| #1863 | 137 |