Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
290 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 59 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. #16863420 | C4 | semidirect |
| 8. C42×Dic67 | C4 | semidirect |
| 10. #16863189 | C4 | semidirect |
| 13. #356×C67 | C4 | semidirect |
| 123. C67 | #7497 | semidirect |
| 131. #356 | Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561874 | 2 |
| #22561038 | 2 |
| C67×#2132 | 2 |
| #7497 | 67 |