Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
434 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 71 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. #22561900 | C2 | semidirect |
| 3. #22560757 | C2 | semidirect |
| 4. #22560754 | C2 | semidirect |
| 5. #22560431 | C2 | semidirect |
| 6. #22558331 | C2 | semidirect |
| 7. C67×#2134 | C2 | semidirect |
| 202. #2134 | D67 | semidirect |
| 207. C67 | #13429 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571070 | 2 |
| #22561900 | 2 |
| #22560757 | 2 |
| #22560754 | 2 |
| #22560431 | 2 |
| #22558331 | 2 |
| C67×#2134 | 2 |
| #13429 | 67 |