Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
292 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 118 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 |
|---|---|---|
| 20. C2×#11764047 | Q8 | semidirect |
| 32. C2×Q8×C137 | C8 | semidirect |
| 70. C137 | #1984 | semidirect |
| 89. C2×Q8 | #11764047 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#11764047 | 2 |
| C2×C4×#11764047 | 2 |
| #22578269 | 2 |
| C2×Q8×Dic137 | 2 |
| #1984 | 137 |