Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
344 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 344 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. #22561963 | C2 | semidirect |
| 3. #22558971 | C2 | semidirect |
| 4. #22558265 | C2 | semidirect |
| 5. #22558263 | C2 | semidirect |
| 6. #22558255 | C2 | semidirect |
| 7. C67×#1361 | C2 | semidirect |
| 144. #1361 | D67 | semidirect |
| 145. C67 | #11985 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570786 | 2 |
| #22561963 | 2 |
| #22558971 | 2 |
| #22558265 | 2 |
| #22558263 | 2 |
| #22558255 | 2 |
| C67×#1361 | 2 |
| #11985 | 67 |