Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
466 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 101 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×#16863210 | C2 | semidirect |
| 3. #22561937 | C2 | semidirect |
| 4. #22561924 | C2 | semidirect |
| 5. #22561813 | C2 | semidirect |
| 6. #22560332 | C2 | semidirect |
| 7. C67×#2145 | C2 | semidirect |
| 13. #16863781 | C4 | semidirect |
| 14. #16863771 | C4 | semidirect |
| 47. C2×C67⋊C16 | D4 | semidirect |
| 63. M32×C67 | D4 | semidirect |
| 177. #2145 | D67 | semidirect |
| 182. C67 | #13215 | semidirect |
| 233. M32 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570696 | 2 |
| C2×#16863210 | 2 |
| #22561937 | 2 |
| #22561924 | 2 |
| #22561813 | 2 |
| #22560332 | 2 |
| C67×#2145 | 2 |
| #13215 | 67 |