Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
460 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22560414 | C2 | semidirect |
| 5. #22558097 | C2 | semidirect |
| 6. #22558096 | C2 | semidirect |
| 7. C67×#1855 | C2 | semidirect |
| 138. C22×D67 | #108 | semidirect |
| 210. #1855 | D67 | semidirect |
| 214. C67 | #8859 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569236 | 2 |
| #22560506 | 2 |
| #22560414 | 2 |
| #22558525 | 2 |
| #22558097 | 2 |
| #22558096 | 2 |
| C67×#1855 | 2 |
| #8859 | 67 |