Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
270 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 16. #16863118 | C4 | semidirect |
| 17. #16863117 | C4 | semidirect |
| 132. C67 | #8794 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22560380 | 2 |
| #22560339 | 2 |
| #22558502 | 2 |
| #22558069 | 2 |
| #22558068 | 2 |
| #22558067 | 2 |
| C67×#1286 | 2 |
| #8794 | 67 |