Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
466 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 107 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. C2×#16863208 | C2 | semidirect |
| 3. #22561944 | C2 | semidirect |
| 4. #22561936 | C2 | semidirect |
| 5. #22561924 | C2 | semidirect |
| 6. #22561814 | C2 | semidirect |
| 7. C67×#1833 | C2 | semidirect |
| 15. #16863780 | C4 | semidirect |
| 16. #16863773 | C4 | semidirect |
| 53. #14523983 | D4 | semidirect |
| 55. C2×C67⋊C16 | D4 | semidirect |
| 181. #1833 | D67 | semidirect |
| 182. C67 | #13215 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570695 | 2 |
| C2×#16863208 | 2 |
| #22561944 | 2 |
| #22561936 | 2 |
| #22561924 | 2 |
| #22561814 | 2 |
| C67×#1833 | 2 |
| #13215 | 67 |