Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
564 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 1. #22571147 | C2 | semidirect |
| 3. #22561033 | C2 | semidirect |
| 4. #22558773 | C2 | semidirect |
| 5. #22558769 | C2 | semidirect |
| 6. #22558054 | C2 | semidirect |
| 7. C67×#3135 | C2 | semidirect |
| 199. #3135 | D67 | semidirect |
| 204. C67 | #10219 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571147 | 2 |
| #22571124 | 2 |
| #22561033 | 2 |
| #22558773 | 2 |
| #22558769 | 2 |
| #22558054 | 2 |
| C67×#3135 | 2 |
| #10219 | 67 |