Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
502 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 81 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. #22571597 | C2 | semidirect |
| 2. #22571409 | C2 | semidirect |
| 4. #22561040 | C2 | semidirect |
| 5. #22558722 | C2 | semidirect |
| 6. #22558718 | C2 | semidirect |
| 7. C67×#1307 | C2 | semidirect |
| 209. #1307 | D67 | semidirect |
| 210. C67 | #10214 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571597 | 2 |
| #22571409 | 2 |
| #22571206 | 2 |
| #22561040 | 2 |
| #22558722 | 2 |
| #22558718 | 2 |
| C67×#1307 | 2 |
| #10214 | 67 |