Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
946 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 946 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. #22571587 | C2 | semidirect |
| 2. #22570534 | C2 | semidirect |
| 3. #22559360 | C2 | semidirect |
| 4. #22559298 | C2 | semidirect |
| 5. #22558947 | C2 | semidirect |
| 6. #22558660 | C2 | semidirect |
| 7. C67×#3548 | C2 | semidirect |
| 170. #3548 | D67 | semidirect |
| 177. C67 | #18696 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571587 | 2 |
| #22570534 | 2 |
| #22559360 | 2 |
| #22559298 | 2 |
| #22558947 | 2 |
| #22558660 | 2 |
| C67×#3548 | 2 |
| #18696 | 67 |