Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
146 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 146 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 |
|---|---|---|
| 45. #11764040 | Q16 | semidirect |
| 70. C137 | #1692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577799 | 2 |
| #22577698 | 2 |
| #22577534 | 2 |
| #22577155 | 2 |
| #22577151 | 2 |
| #22577149 | 2 |
| #462×C137 | 2 |
| #1692 | 137 |