Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
674 conjugacy classes of subgroups; only the 259 normal subgroups are shown.
This group has 674 conjugacy classes of subgroups — too many to draw. Only its 259 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 |
|---|---|---|
| 21. #498×C67 | C4 | semidirect |
| 111. C67 | #22253 | semidirect |
| 113. #498 | Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562958 | 2 |
| #22561183 | 2 |
| #22560796 | 2 |
| #22560789 | 2 |
| #22560340 | 2 |
| #22559960 | 2 |
| C2×#498×C67 | 2 |
| #22253 | 67 |