Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
566 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 113 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×#16863216 | C2 | semidirect |
| 3. C2×#16863210 | C2 | semidirect |
| 4. C2×#16863209 | C2 | semidirect |
| 5. #22561924 | C2 | semidirect |
| 6. #22560090 | C2 | semidirect |
| 7. C67×#2140 | C2 | semidirect |
| 13. #16863771 | C4 | semidirect |
| 47. #14523979 | D4 | semidirect |
| 64. #107×C67 | D4 | semidirect |
| 178. #2140 | D67 | semidirect |
| 180. C67 | #13261 | semidirect |
| 233. #107 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863771 | 2 |
| C2×#16863216 | 2 |
| C2×#16863210 | 2 |
| C2×#16863209 | 2 |
| #22561924 | 2 |
| #22560090 | 2 |
| C67×#2140 | 2 |
| #13261 | 67 |