Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
248 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 248 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 |
|---|---|---|
| 12. C4×C8×C137 | C4 | semidirect |
| 53. C137 | #1846 | semidirect |
| 65. C4×C8 | Dic137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984022 | 2 |
| C2×#17984020 | 2 |
| #22577269 | 2 |
| C2×C4×C8×C137 | 2 |
| #1846 | 137 |