Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
150 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 56. C8×C137 | Q16 | semidirect |
| 70. C137 | #1672 | semidirect |
| 127. C8 | #14555500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577695 | 2 |
| #22577610 | 2 |
| C8×Dic274 | 2 |
| #22577154 | 2 |
| #22577152 | 2 |
| #22577149 | 2 |
| #498×C137 | 2 |
| #1672 | 137 |