Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
148 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 148 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 |
|---|---|---|
| 11. #17984034 | C4 | semidirect |
| 63. C137 | #2176 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984034 | 2 |
| Q16×Dic137 | 2 |
| #22577497 | 2 |
| #22577230 | 2 |
| #22577208 | 2 |
| #22577178 | 2 |
| #358×C137 | 2 |
| #2176 | 137 |