Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
256 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 63 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. #22562357 | C2 | semidirect |
| 3. #22559798 | C2 | semidirect |
| 4. #22559003 | C2 | semidirect |
| 5. #22558272 | C2 | semidirect |
| 6. #22558268 | C2 | semidirect |
| 7. C67×#1361 | C2 | semidirect |
| 50. D536 | SD16 | semidirect |
| 121. #1361 | D67 | semidirect |
| 122. C67 | #12418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22562357 | 2 |
| #22562241 | 2 |
| #22559798 | 2 |
| #22559003 | 2 |
| #22558272 | 2 |
| #22558268 | 2 |
| C67×#1361 | 2 |
| #12418 | 67 |