Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1130 conjugacy classes of subgroups; only the 403 normal subgroups are shown.
This group has 1130 conjugacy classes of subgroups — too many to draw. Only its 403 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. #22562572 | C2 | semidirect |
| 4. C4×#14523975 | C2 | semidirect |
| 5. #22560040 | C2 | semidirect |
| 7. C67×#1726 | C2 | semidirect |
| 11. C4×#11761617 | C4 | semidirect |
| 30. C4×Dic134 | C2×C4 | semidirect |
| 40. #14523975 | C2×C4 | semidirect |
| 41. #14523968 | C2×C4 | semidirect |
| 49. C4×C8×C67 | C2×C4 | semidirect |
| 62. #11761617 | C42 | semidirect |
| 128. #1726 | D67 | semidirect |
| 129. C67 | #20506 | semidirect |
| 169. C4×C8 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#11761617 | 2 |
| #22562572 | 2 |
| #22562571 | 2 |
| C4×#14523975 | 2 |
| #22560040 | 2 |
| #22560035 | 2 |
| C67×#1726 | 2 |
| #20506 | 67 |