Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
306 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 306 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. #22562009 | C2 | semidirect |
| 3. #22560345 | C2 | semidirect |
| 4. #22558228 | C2 | semidirect |
| 5. #22558226 | C2 | semidirect |
| 157. C67 | #11866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570774 | 2 |
| #22562009 | 2 |
| #22560345 | 2 |
| #22558228 | 2 |
| #22558226 | 2 |
| #22558224 | 2 |
| C67×#1349 | 2 |
| #11866 | 67 |