Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
314 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 79 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. #16863800 | C4 | semidirect |
| 10. #16863774 | C4 | semidirect |
| 14. Q16×Dic67 | C4 | semidirect |
| 15. #16863490 | C4 | semidirect |
| 162. C67 | #11859 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570790 | 2 |
| #22562009 | 2 |
| #22560338 | 2 |
| #22558222 | 2 |
| #22558221 | 2 |
| #22558220 | 2 |
| C67×#1348 | 2 |
| #11859 | 67 |