Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
308 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 11. #17984053 | C4 | semidirect |
| 58. Dic274 | C4⋊C4 | semidirect |
| 102. Dic137 | #103 | semidirect |
| 110. C137 | #1803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984053 | 2 |
| C2×#17984017 | 2 |
| C2×#17984013 | 2 |
| C2×#17984011 | 2 |
| #22577272 | 2 |
| #22577165 | 2 |
| #340×C137 | 2 |
| #1803 | 137 |