Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
334 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 4. #22558189 | C2 | semidirect |
| 5. Q8⋊(C67⋊C16) | C2 | semidirect |
| 6. #22558187 | C2 | semidirect |
| 7. C67×Q8⋊C16 | C2 | semidirect |
| 156. Q8⋊C16 | D67 | semidirect |
| 157. C67 | #11639 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×Q8×D67 | 2 |
| #22562011 | 2 |
| #22562006 | 2 |
| #22558189 | 2 |
| Q8⋊(C67⋊C16) | 2 |
| #22558187 | 2 |
| C67×Q8⋊C16 | 2 |
| #11639 | 67 |