Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
436 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 3. #22561148 | C2 | semidirect |
| 5. #22558657 | C2 | semidirect |
| 6. #22558109 | C2 | semidirect |
| 7. C67×#1283 | C2 | semidirect |
| 213. #1283 | D67 | semidirect |
| 214. C67 | #9051 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570291 | 2 |
| #22569345 | 2 |
| #22561148 | 2 |
| #22558798 | 2 |
| #22558657 | 2 |
| #22558109 | 2 |
| C67×#1283 | 2 |
| #9051 | 67 |