Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
426 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 109 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×#16863225 | C2 | semidirect |
| 3. C2×#16863204 | C2 | semidirect |
| 4. C2×C16×Dic67 | C2 | semidirect |
| 5. #22561098 | C2 | semidirect |
| 6. #22561095 | C2 | semidirect |
| 7. C2×#359×C67 | C2 | semidirect |
| 11. C2×#14523989 | C4 | semidirect |
| 12. C2×#14523987 | C4 | semidirect |
| 13. C2×#14523986 | C4 | semidirect |
| 14. C2×#14523984 | C4 | semidirect |
| 182. C2×#359 | D67 | semidirect |
| 186. C67 | #13241 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863826 | 2 |
| C2×#16863225 | 2 |
| C2×#16863204 | 2 |
| C2×C16×Dic67 | 2 |
| #22561098 | 2 |
| #22561095 | 2 |
| C2×#359×C67 | 2 |
| #13241 | 67 |