Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
348 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 75 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. #22561201 | C2 | semidirect |
| 4. #22558810 | C2 | semidirect |
| 6. #22558080 | C2 | semidirect |
| 7. C67×#1569 | C2 | semidirect |
| 168. #1569 | D67 | semidirect |
| 173. C67 | #10497 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571401 | 2 |
| #22561201 | 2 |
| #22558929 | 2 |
| #22558810 | 2 |
| #22558800 | 2 |
| #22558080 | 2 |
| C67×#1569 | 2 |
| #10497 | 67 |