Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
748 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 748 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. #22561042 | C2 | semidirect |
| 3. #22558940 | C2 | semidirect |
| 4. #22558932 | C2 | semidirect |
| 5. #22558722 | C2 | semidirect |
| 6. #22558718 | C2 | semidirect |
| 7. C67×#1536 | C2 | semidirect |
| 9. #16864107 | C4 | semidirect |
| 12. #16864066 | C4 | semidirect |
| 226. #1536 | D67 | semidirect |
| 229. C67 | #8493 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22574607 | 2 |
| #22561042 | 2 |
| #22558940 | 2 |
| #22558932 | 2 |
| #22558722 | 2 |
| #22558718 | 2 |
| C67×#1536 | 2 |
| #8493 | 67 |