Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
318 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 33. #14523983 | Q8 | semidirect |
| 37. C2×C67⋊C16 | Q8 | semidirect |
| 51. #108×C67 | Q8 | semidirect |
| 141. C67 | #13455 | semidirect |
| 178. #108 | Dic134 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570748 | 2 |
| #22561995 | 2 |
| C2×#16863221 | 2 |
| #22558319 | 2 |
| #22558306 | 2 |
| #22558298 | 2 |
| C67×#1952 | 2 |
| #13455 | 67 |