Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
354 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 83 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. #22562010 | C2 | semidirect |
| 3. #334×D67 | C2 | semidirect |
| 4. #22558177 | C2 | semidirect |
| 5. #22558176 | C2 | semidirect |
| 6. #22558175 | C2 | semidirect |
| 7. C67×#1333 | C2 | semidirect |
| 166. #1333 | D67 | semidirect |
| 167. C67 | #11654 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570785 | 2 |
| #22562010 | 2 |
| #334×D67 | 2 |
| #22558177 | 2 |
| #22558176 | 2 |
| #22558175 | 2 |
| C67×#1333 | 2 |
| #11654 | 67 |