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. C22×D1072 | C2 | semidirect |
| 2. #22562521 | C2 | direct (N × H) |
| 3. C2×#16863233 | C2 | semidirect |
| 4. C2×#16863231 | C2 | semidirect |
| 5. C2×#16863230 | C2 | semidirect |
| 6. C2×#508×C67 | C2 | semidirect |
| 11. C2×D1072 | C22 | semidirect |
| 12. #16863233 | C22 | semidirect |
| 13. #16863231 | C22 | semidirect |
| 14. #16863230 | C22 | semidirect |
| 15. C2×C67⋊C32 | C22 | semidirect |
| 18. #508×C67 | C22 | semidirect |
| 19. C2×Q32×C67 | C22 | semidirect |
| 21. C2×D16×C67 | C22 | semidirect |
| 31. C67⋊C32 | C23 | semidirect |
| 40. Q32×C67 | C23 | semidirect |
| 43. D16×C67 | C23 | semidirect |
| 112. C2×C67 | #2263 | semidirect |
| 115. C2×#508 | D67 | semidirect |
| 121. C67 | C2×#2263 | semidirect |
| 125. #508 | C2×D67 | semidirect |
| 126. C2×Q32 | C2×D67 | semidirect |
| 132. C2×D16 | C2×D67 | semidirect |
| 151. Q32 | C22×D67 | semidirect |
| 157. D16 | C22×D67 | semidirect |
| 227. C2 | #22562521 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1072 | 2 |
| #22562521 | 2 |
| C2×#16863233 | 2 |
| C2×#16863231 | 2 |
| C2×#16863230 | 2 |
| C2×#508×C67 | 2 |
| C2×#2263 | 67 |