Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
396 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 73 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. #22561828 | C2 | semidirect |
| 3. #22560254 | C2 | semidirect |
| 4. #22558195 | C2 | semidirect |
| 5. #22558194 | C2 | semidirect |
| 6. #22558193 | C2 | semidirect |
| 7. C67×#1339 | C2 | semidirect |
| 8. C2×D8×D67 | C4 | semidirect |
| 12. #16863650 | C4 | semidirect |
| 14. #16863646 | C4 | semidirect |
| 18. #16863431 | C4 | semidirect |
| 21. #16863178 | C22 | semidirect |
| 23. #16863153 | C22 | semidirect |
| 25. #349×C67 | C22 | semidirect |
| 26. H(3,ℤ/4)×C67 | C22 | semidirect |
| 197. #1339 | D67 | semidirect |
| 198. C67 | #11868 | semidirect |
| 215. #349 | C2×D67 | semidirect |
| 217. H(3,ℤ/4) | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569855 | 2 |
| #22561828 | 2 |
| #22560254 | 2 |
| #22558195 | 2 |
| #22558194 | 2 |
| #22558193 | 2 |
| C67×#1339 | 2 |
| #11868 | 67 |