Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
568 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 91 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. #22569237 | C2 | semidirect |
| 3. #22558833 | C2 | semidirect |
| 4. #22558549 | C2 | semidirect |
| 5. #22558066 | C2 | semidirect |
| 6. #22558064 | C2 | semidirect |
| 7. C67×#1533 | C2 | semidirect |
| 61. #14523954 | D4 | semidirect |
| 79. #97×C67 | D4 | semidirect |
| 244. #1533 | D67 | semidirect |
| 248. C67 | #9447 | semidirect |
| 317. #97 | C22⋊D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569237 | 2 |
| #22565181 | 2 |
| #22558833 | 2 |
| #22558549 | 2 |
| #22558066 | 2 |
| #22558064 | 2 |
| C67×#1533 | 2 |
| #9447 | 67 |