Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
226 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22559826 | C2 | semidirect |
| 5. #22558272 | C2 | semidirect |
| 6. #22558268 | C2 | semidirect |
| 7. C67×#1365 | C2 | semidirect |
| 110. #1365 | D67 | semidirect |
| 111. C67 | #12499 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562357 | 2 |
| #22562353 | 2 |
| #22559826 | 2 |
| #22559093 | 2 |
| #22558272 | 2 |
| #22558268 | 2 |
| C67×#1365 | 2 |
| #12499 | 67 |