Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
142 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 27 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 |
|---|---|---|
| 7. #494×C67 | C4 | semidirect |
| 10. #322×C67 | C4 | semidirect |
| 64. C67 | #7528 | semidirect |
| 66. #494 | Dic67 | semidirect |
| 71. #322 | Dic67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22558376 | 2 |
| #22558374 | 2 |
| C67×#1722 | 2 |
| #7528 | 67 |