Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
4038 conjugacy classes of subgroups; only the 827 normal subgroups are shown.
This group has 4038 conjugacy classes of subgroups — too many to draw. Only its 827 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. C23×#11761616 | C2 | semidirect |
| 2. C23×#11761613 | C2 | semidirect |
| 3. C22×#14524031 | C2 | semidirect |
| 4. C2×#16863783 | C2 | direct (N × H) |
| 5. C22×#14523954 | C2 | semidirect |
| 6. C22×#127×C67 | C2 | semidirect |
| 10. C22×#11761616 | C22 | semidirect |
| 12. C22×#11761613 | C22 | semidirect |
| 15. C2×#14524031 | C22 | semidirect |
| 17. #16863783 | C22 | direct (N × H) |
| 18. C2×#14523954 | C22 | semidirect |
| 22. C2×#127×C67 | C22 | semidirect |
| 33. C2×#11761616 | C23 | semidirect |
| 35. C2×#11761613 | C23 | semidirect |
| 36. C22×C67⋊C8 | D4 | semidirect |
| 39. #14524031 | C23 | semidirect |
| 41. #14523954 | C23 | semidirect |
| 52. #127×C67 | C23 | semidirect |
| 70. C2×C67⋊C8 | C2×D4 | semidirect |
| 118. C67⋊C8 | C22×D4 | semidirect |
| 122. C22×C67 | #496 | semidirect |
| 135. C2×C67 | C2×#496 | semidirect |
| 141. C22×#127 | D67 | semidirect |
| 145. C67 | C22×#496 | semidirect |
| 156. C2×#127 | C2×D67 | semidirect |
| 187. #127 | C22×D67 | semidirect |
| 264. C22 | #16863783 | direct (N × H) |
| 274. C2 | C2×#16863783 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11761616 | 2 |
| C23×#11761613 | 2 |
| C22×#14524031 | 2 |
| C2×#16863783 | 2 |
| C22×#14523954 | 2 |
| C22×#127×C67 | 2 |
| C22×#496 | 67 |