Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
306 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22562007 | C2 | semidirect |
| 3. #22558954 | C2 | semidirect |
| 4. #22558262 | C2 | semidirect |
| 5. #22558260 | C2 | semidirect |
| 6. #22558252 | C2 | semidirect |
| 7. C67×#1360 | C2 | semidirect |
| 155. #1360 | D67 | semidirect |
| 156. C67 | #11943 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570776 | 2 |
| #22562007 | 2 |
| #22558954 | 2 |
| #22558262 | 2 |
| #22558260 | 2 |
| #22558252 | 2 |
| C67×#1360 | 2 |
| #11943 | 67 |