Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
336 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 141 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×#17984020 | C2 | semidirect |
| 3. #22577166 | C2 | semidirect |
| 11. C22×C8×C137 | C4 | semidirect |
| 48. C8×C137 | C22⋊C4 | semidirect |
| 52. C22×C137 | #106 | semidirect |
| 67. C137 | #1807 | semidirect |
| 75. C22×C8 | Dic137 | semidirect |
| 116. C8 | C22⋊Dic137 | semidirect |
| 120. C22 | #17984020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984020 | 2 |
| #22577263 | 2 |
| #22577166 | 2 |
| C23×C8×C137 | 2 |
| #1807 | 137 |