Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
492 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 89 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. #22570755 | C2 | semidirect |
| 4. #22561052 | C2 | semidirect |
| 6. #22558629 | C2 | semidirect |
| 7. C67×#1299 | C2 | semidirect |
| 186. #1299 | D67 | semidirect |
| 187. C67 | #10116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571597 | 2 |
| #22571339 | 2 |
| #22570755 | 2 |
| #22561052 | 2 |
| #22558800 | 2 |
| #22558629 | 2 |
| C67×#1299 | 2 |
| #10116 | 67 |