Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
364 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 79 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. #22560110 | C2 | semidirect |
| 4. #22558225 | C2 | semidirect |
| 5. #22558224 | C2 | semidirect |
| 6. #22558223 | C2 | semidirect |
| 7. C67×#1349 | C2 | semidirect |
| 166. #1349 | D67 | semidirect |
| 167. C67 | #11751 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570783 | 2 |
| #22562009 | 2 |
| #22560110 | 2 |
| #22558225 | 2 |
| #22558224 | 2 |
| #22558223 | 2 |
| C67×#1349 | 2 |
| #11751 | 67 |