Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
934 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 934 conjugacy classes of subgroups — too many to draw. Only its 183 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 |
|---|---|---|
| 3. #22559251 | C2 | semidirect |
| 5. #22558721 | C2 | semidirect |
| 6. #22558553 | C2 | semidirect |
| 7. C67×#3502 | C2 | semidirect |
| 183. #3502 | D67 | semidirect |
| 190. C67 | #18188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570304 | 2 |
| #22563492 | 2 |
| #22559251 | 2 |
| #22559149 | 2 |
| #22558721 | 2 |
| #22558553 | 2 |
| C67×#3502 | 2 |
| #18188 | 67 |