Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
922 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 922 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. #22561149 | C2 | semidirect |
| 3. #22558905 | C2 | semidirect |
| 4. #22558904 | C2 | semidirect |
| 5. #22558819 | C2 | semidirect |
| 6. #22558552 | C2 | semidirect |
| 7. C67×#1530 | C2 | semidirect |
| 230. #1530 | D67 | semidirect |
| 232. C67 | #8459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22573975 | 2 |
| #22561149 | 2 |
| #22558905 | 2 |
| #22558904 | 2 |
| #22558819 | 2 |
| #22558552 | 2 |
| C67×#1530 | 2 |
| #8459 | 67 |