Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
218 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 69 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. #22562491 | C2 | semidirect |
| 5. #22558268 | C2 | semidirect |
| 6. #22558265 | C2 | semidirect |
| 7. C67×#1372 | C2 | semidirect |
| 65. C16×C67 | SD16 | semidirect |
| 107. #1372 | D67 | semidirect |
| 110. C67 | #12453 | semidirect |
| 168. C16 | #11761617 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562491 | 2 |
| C16×D268 | 2 |
| #22559609 | 2 |
| #22559599 | 2 |
| #22558268 | 2 |
| #22558265 | 2 |
| C67×#1372 | 2 |
| #12453 | 67 |