Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
224 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 65 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. #22562482 | C2 | semidirect |
| 5. #22558280 | C2 | semidirect |
| 6. #22558263 | C2 | semidirect |
| 7. C67×#1364 | C2 | semidirect |
| 58. C67⋊C16 | SD16 | semidirect |
| 111. #1364 | D67 | semidirect |
| 112. C67 | #12451 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562482 | 2 |
| #22562028 | 2 |
| #22559599 | 2 |
| #22559595 | 2 |
| #22558280 | 2 |
| #22558263 | 2 |
| C67×#1364 | 2 |
| #12451 | 67 |