Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
156 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 44. Dic274 | Q16 | semidirect |
| 72. C137 | #1670 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577782 | 2 |
| #22577689 | 2 |
| #22577685 | 2 |
| #22577527 | 2 |
| #22577155 | 2 |
| #22577150 | 2 |
| #332×C137 | 2 |
| #1670 | 137 |