Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
152 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 42. C8×C137 | Q16 | semidirect |
| 54. C137 | #1694 | semidirect |
| 97. C8 | #14555500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577610 | 2 |
| #22577533 | 2 |
| #22577154 | 2 |
| #22577149 | 2 |
| #500×C137 | 2 |
| #1694 | 137 |