Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
338 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 109 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. #333×C67 | C4 | semidirect |
| 22. #332×C67 | C4 | semidirect |
| 146. C67 | #9579 | semidirect |
| 159. #333 | Dic67 | semidirect |
| 160. #332 | Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22561187 | 2 |
| C4⋊C8×Dic67 | 2 |
| #22558980 | 2 |
| #22558612 | 2 |
| #22558106 | 2 |
| #22558041 | 2 |
| C67×#1542 | 2 |
| #9579 | 67 |