Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
372 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 61 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. #22562287 | C2 | semidirect |
| 3. #22559816 | C2 | semidirect |
| 4. #22558245 | C2 | semidirect |
| 5. #22558182 | C2 | semidirect |
| 6. #22558181 | C2 | semidirect |
| 7. C67×#2214 | C2 | semidirect |
| 17. #16863217 | C22 | semidirect |
| 19. C8×C67⋊C8 | C22 | semidirect |
| 21. #494×C67 | C22 | semidirect |
| 23. #364×C67 | C22 | semidirect |
| 147. #2214 | D67 | semidirect |
| 152. C67 | #12312 | semidirect |
| 157. #494 | C2×D67 | semidirect |
| 166. #364 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22572009 | 2 |
| #22562287 | 2 |
| #22559816 | 2 |
| #22558245 | 2 |
| #22558182 | 2 |
| #22558181 | 2 |
| C67×#2214 | 2 |
| #12312 | 67 |