Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
826 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 826 conjugacy classes of subgroups — too many to draw. Only its 203 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. #22568926 | C2 | semidirect |
| 3. #22561036 | C2 | semidirect |
| 4. #22560537 | C2 | semidirect |
| 5. #22559957 | C2 | semidirect |
| 6. C67×#1838 | C2 | semidirect |
| 10. #16863790 | C4 | semidirect |
| 11. #16863785 | C4 | semidirect |
| 111. #1838 | D67 | semidirect |
| 113. C67 | #22283 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570655 | 2 |
| #22568926 | 2 |
| #22561036 | 2 |
| #22560537 | 2 |
| #22559957 | 2 |
| C67×#1838 | 2 |
| #22283 | 67 |