Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
408 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 408 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. #22560362 | C2 | semidirect |
| 3. #22558902 | C2 | semidirect |
| 4. #22558718 | C2 | semidirect |
| 5. #22558717 | C2 | semidirect |
| 6. #22558078 | C2 | semidirect |
| 7. C67×#1551 | C2 | semidirect |
| 169. #1551 | D67 | semidirect |
| 173. C67 | #10512 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571516 | 2 |
| #22560362 | 2 |
| #22558902 | 2 |
| #22558718 | 2 |
| #22558717 | 2 |
| #22558078 | 2 |
| C67×#1551 | 2 |
| #10512 | 67 |