Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
416 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22558900 | C2 | semidirect |
| 5. #22558611 | C2 | semidirect |
| 6. #22558060 | C2 | semidirect |
| 7. C67×#1950 | C2 | semidirect |
| 178. #1950 | D67 | semidirect |
| 184. C67 | #10553 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570584 | 2 |
| #22558900 | 2 |
| #22558878 | 2 |
| C2×#16863139 | 2 |
| #22558611 | 2 |
| #22558060 | 2 |
| C67×#1950 | 2 |
| #10553 | 67 |