Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
4638 conjugacy classes of subgroups; only the 987 normal subgroups are shown.
This group has 4638 conjugacy classes of subgroups — too many to draw. Only its 987 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×#11761613 | C2 | semidirect |
| 2. C22×#14524040 | C2 | semidirect |
| 3. C2×#16863772 | C2 | direct (N × H) |
| 4. C22×C4×C67⋊C8 | C2 | semidirect |
| 5. C22×#127×C67 | C2 | semidirect |
| 9. C22×#11761613 | C22 | semidirect |
| 12. C2×#14524040 | C22 | semidirect |
| 13. #16863772 | C22 | direct (N × H) |
| 14. C2×C4×C67⋊C8 | C22 | semidirect |
| 18. C2×#127×C67 | C22 | semidirect |
| 27. C2×#11761613 | C23 | semidirect |
| 28. C22×C67⋊C8 | D4 | semidirect |
| 31. #14524040 | C23 | semidirect |
| 32. C4×C67⋊C8 | C23 | semidirect |
| 42. #127×C67 | C23 | semidirect |
| 55. C2×C67⋊C8 | C2×D4 | semidirect |
| 67. C22×C4×C67 | D8 | semidirect |
| 89. C2×C4×C67 | C2×D8 | semidirect |
| 97. C67⋊C8 | C22×D4 | semidirect |
| 101. C22×C67 | #493 | semidirect |
| 109. C4×C67 | C22×D8 | semidirect |
| 113. C2×C67 | C2×#493 | semidirect |
| 119. C22×#127 | D67 | semidirect |
| 122. C67 | C22×#493 | semidirect |
| 133. C2×#127 | C2×D67 | semidirect |
| 158. #127 | C22×D67 | semidirect |
| 181. C22×C4 | #11761613 | semidirect |
| 209. C2×C4 | C2×#11761613 | semidirect |
| 221. C22 | #16863772 | direct (N × H) |
| 226. C4 | C22×#11761613 | semidirect |
| 230. C2 | C2×#16863772 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11761613 | 2 |
| C22×#14524040 | 2 |
| C2×#16863772 | 2 |
| C22×C4×C67⋊C8 | 2 |
| C22×#127×C67 | 2 |
| C22×#493 | 67 |