Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
330 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22558985 | C2 | semidirect |
| 5. #22558105 | C2 | semidirect |
| 6. #22558067 | C2 | semidirect |
| 7. C67×#1286 | C2 | semidirect |
| 153. #1286 | D67 | semidirect |
| 154. C67 | #10637 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22560216 | 2 |
| #22560198 | 2 |
| #22558985 | 2 |
| #22558599 | 2 |
| #22558105 | 2 |
| #22558067 | 2 |
| C67×#1286 | 2 |
| #10637 | 67 |