Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
422 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 9. #16863775 | C4 | semidirect |
| 10. #16863748 | C4 | semidirect |
| 78. C2×C67⋊C8 | Q16 | semidirect |
| 163. C67 | #9290 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571154 | 2 |
| #22569150 | 2 |
| #22561181 | 2 |
| #22558893 | 2 |
| #22558067 | 2 |
| #22558039 | 2 |
| C67×#1518 | 2 |
| #9290 | 67 |