Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
686 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 115 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. #22558523 | C2 | semidirect |
| 3. #22558136 | C2 | semidirect |
| 4. C67×#1458 | C2 | semidirect |
| 27. C22×D268 | C8 | semidirect |
| 187. #1458 | D67 | semidirect |
| 189. C67 | #11427 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562789 | 2 |
| #22558523 | 2 |
| #22558136 | 2 |
| C67×#1458 | 2 |
| #11427 | 67 |