Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
306 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 91. Q8×C67 | Q32 | semidirect |
| 133. C67 | #12334 | semidirect |
| 221. Q8 | #14523989 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573215 | 2 |
| #22562461 | 2 |
| #22562256 | 2 |
| #22558257 | 2 |
| Q8⋊(C67⋊C16) | 2 |
| #22558172 | 2 |
| C67×#1670 | 2 |
| #12334 | 67 |