Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
372 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 99 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. #22560346 | C2 | semidirect |
| 3. #22558998 | C2 | semidirect |
| 6. #22558047 | C2 | semidirect |
| 7. C67×#1299 | C2 | semidirect |
| 172. #1299 | D67 | semidirect |
| 174. C67 | #8901 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569339 | 2 |
| #22560346 | 2 |
| #22558998 | 2 |
| #22558649 | 2 |
| #22558589 | 2 |
| #22558047 | 2 |
| C67×#1299 | 2 |
| #8901 | 67 |