Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
728 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 163 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. #22570923 | C2 | semidirect |
| 2. #22570602 | C2 | semidirect |
| 3. #22570590 | C2 | semidirect |
| 4. #22559859 | C2 | semidirect |
| 5. #22559853 | C2 | semidirect |
| 6. #22559847 | C2 | semidirect |
| 7. #22559820 | C2 | semidirect |
| 8. #22558512 | C2 | semidirect |
| 168. C67 | #19754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570923 | 2 |
| #22570602 | 2 |
| #22570590 | 2 |
| #22559859 | 2 |
| #22559853 | 2 |
| #22559847 | 2 |
| #22559820 | 2 |
| #22558512 | 2 |
| C67×#3184 | 2 |
| #19754 | 67 |