Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
598 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 95 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. #22570241 | C2 | semidirect |
| 3. #22563493 | C2 | semidirect |
| 4. #22561040 | C2 | semidirect |
| 5. #22558637 | C2 | semidirect |
| 6. #22558037 | C2 | semidirect |
| 7. C67×#1486 | C2 | semidirect |
| 222. #1486 | D67 | semidirect |
| 224. C67 | #10013 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570241 | 2 |
| #22570209 | 2 |
| #22563493 | 2 |
| #22561040 | 2 |
| #22558637 | 2 |
| #22558037 | 2 |
| C67×#1486 | 2 |
| #10013 | 67 |