Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
732 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 732 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. #22561190 | C2 | semidirect |
| 3. #22558932 | C2 | semidirect |
| 4. #22558931 | C2 | semidirect |
| 5. #22558846 | C2 | semidirect |
| 6. #22558716 | C2 | semidirect |
| 7. C67×#1505 | C2 | semidirect |
| 13. #16864051 | C4 | semidirect |
| 14. #16864050 | C4 | semidirect |
| 224. #1505 | D67 | semidirect |
| 225. C67 | #8494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22574607 | 2 |
| #22561190 | 2 |
| #22558932 | 2 |
| #22558931 | 2 |
| #22558846 | 2 |
| #22558716 | 2 |
| C67×#1505 | 2 |
| #8494 | 67 |