Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
414 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 77 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. #22561141 | C2 | semidirect |
| 3. #22558995 | C2 | semidirect |
| 4. #22558905 | C2 | semidirect |
| 5. #22558703 | C2 | semidirect |
| 6. #22558562 | C2 | semidirect |
| 7. C67×#1285 | C2 | semidirect |
| 200. #1285 | D67 | semidirect |
| 201. C67 | #10508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571198 | 2 |
| #22561141 | 2 |
| #22558995 | 2 |
| #22558905 | 2 |
| #22558703 | 2 |
| #22558562 | 2 |
| C67×#1285 | 2 |
| #10508 | 67 |