Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
418 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 418 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. #22562434 | C2 | semidirect |
| 3. #22562353 | C2 | semidirect |
| 4. #22558254 | C2 | semidirect |
| 5. #22558169 | C2 | semidirect |
| 6. D4⋊(C67⋊C16) | C2 | semidirect |
| 7. C67×#1675 | C2 | semidirect |
| 16. C4⋊(C67⋊C16) | C22 | semidirect |
| 19. C4×C67⋊C16 | C22 | semidirect |
| 20. #500×C67 | C22 | semidirect |
| 23. #335×C67 | C22 | semidirect |
| 153. #1675 | D67 | semidirect |
| 157. C67 | #12372 | semidirect |
| 160. #500 | C2×D67 | semidirect |
| 173. #335 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D536 | 2 |
| #22562434 | 2 |
| #22562353 | 2 |
| #22558254 | 2 |
| #22558169 | 2 |
| D4⋊(C67⋊C16) | 2 |
| C67×#1675 | 2 |
| #12372 | 67 |