Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
372 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 372 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 |
|---|---|---|
| 2. #22559000 | C2 | semidirect |
| 5. #22558098 | C2 | semidirect |
| 6. #22558046 | C2 | semidirect |
| 7. C67×#1837 | C2 | semidirect |
| 168. #1837 | D67 | semidirect |
| 174. C67 | #8901 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569339 | 2 |
| #22559000 | 2 |
| #22558646 | 2 |
| #22558592 | 2 |
| #22558098 | 2 |
| #22558046 | 2 |
| C67×#1837 | 2 |
| #8901 | 67 |