Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
316 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 3. #22561703 | C2 | semidirect |
| 4. #22558221 | C2 | semidirect |
| 6. #22558148 | C2 | semidirect |
| 7. C67×#2236 | C2 | semidirect |
| 154. #2236 | D67 | semidirect |
| 160. C67 | #12293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571562 | 2 |
| #22562394 | 2 |
| #22561703 | 2 |
| #22558221 | 2 |
| #22558219 | 2 |
| #22558148 | 2 |
| C67×#2236 | 2 |
| #12293 | 67 |