Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
452 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 1. #22560219 | C2 | semidirect |
| 2. #22558981 | C2 | semidirect |
| 3. #22558858 | C2 | semidirect |
| 4. #22558769 | C2 | semidirect |
| 5. #22558530 | C2 | semidirect |
| 6. #22558069 | C2 | semidirect |
| 199. C67 | #10465 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22560219 | 2 |
| #22558981 | 2 |
| #22558858 | 2 |
| #22558769 | 2 |
| #22558530 | 2 |
| #22558069 | 2 |
| C67×#3036 | 2 |
| #10465 | 67 |