Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
502 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 155 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 |
|---|---|---|
| 1. C2×#16863828 | C2 | semidirect |
| 2. C22×D1072 | C2 | semidirect |
| 3. #22562524 | C2 | direct (N × H) |
| 4. C2×#16863235 | C2 | semidirect |
| 5. C2×D2144 | C2 | semidirect |
| 6. C2×M64×C67 | C2 | semidirect |
| 10. #16863828 | C22 | semidirect |
| 11. C2×Dic536 | C22 | semidirect |
| 16. C2×D1072 | C22 | semidirect |
| 17. C2×D1072 | C22 | semidirect |
| 18. #16863235 | C22 | semidirect |
| 19. D2144 | C22 | semidirect |
| 21. M64×C67 | C22 | semidirect |
| 22. C2×C32×C67 | C22 | semidirect |
| 35. Dic536 | C23 | semidirect |
| 41. D1072 | C23 | semidirect |
| 47. C32×C67 | C23 | semidirect |
| 111. C2×C67 | #2263 | semidirect |
| 120. C2×M64 | D67 | semidirect |
| 121. C67 | C2×#2263 | semidirect |
| 136. M64 | C2×D67 | semidirect |
| 137. C2×C32 | C2×D67 | semidirect |
| 162. C32 | C22×D67 | semidirect |
| 227. C2 | #22562524 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863828 | 2 |
| C22×D1072 | 2 |
| #22562524 | 2 |
| C2×#16863235 | 2 |
| C2×D2144 | 2 |
| C2×M64×C67 | 2 |
| C2×#2263 | 67 |