Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
462 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 103 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. #22569125 | C2 | semidirect |
| 3. #22561946 | C2 | semidirect |
| 4. #22561108 | C2 | semidirect |
| 5. #22558306 | C2 | semidirect |
| 6. #22558299 | C2 | semidirect |
| 7. C67×#2143 | C2 | semidirect |
| 12. C2×#14523989 | C4 | semidirect |
| 13. C2×#14523987 | C4 | semidirect |
| 14. C2×#14523986 | C4 | semidirect |
| 15. C2×#14523984 | C4 | semidirect |
| 186. #2143 | D67 | semidirect |
| 190. C67 | #13016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863826 | 2 |
| #22569125 | 2 |
| #22561946 | 2 |
| #22561108 | 2 |
| #22558306 | 2 |
| #22558299 | 2 |
| C67×#2143 | 2 |
| #13016 | 67 |