Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
384 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 3. #22577708 | C2 | direct (N × H) |
| 91. C2×C137 | #479 | semidirect |
| 95. C137 | C2×#479 | semidirect |
| 187. C2 | #22577708 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984079 | 2 |
| C2×Q8×Dic137 | 2 |
| #22577708 | 2 |
| C2×#17984021 | 2 |
| C2×#17984020 | 2 |
| C2×#17984017 | 2 |
| C2×#17984012 | 2 |
| C2×#103×C137 | 2 |
| C2×#479 | 137 |