Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
954 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 954 conjugacy classes of subgroups — too many to draw. Only its 179 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. #22571592 | C2 | semidirect |
| 3. #22559349 | C2 | semidirect |
| 4. #22559330 | C2 | semidirect |
| 5. #22559287 | C2 | semidirect |
| 6. #22559268 | C2 | semidirect |
| 7. #22558944 | C2 | semidirect |
| 8. #22558664 | C2 | semidirect |
| 9. C67×#3550 | C2 | semidirect |
| 191. #3550 | D67 | semidirect |
| 200. C67 | #18688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571592 | 2 |
| #22570635 | 2 |
| #22559349 | 2 |
| #22559330 | 2 |
| #22559287 | 2 |
| #22559268 | 2 |
| #22558944 | 2 |
| #22558664 | 2 |
| C67×#3550 | 2 |
| #18688 | 67 |