Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
494 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #22561028 | C2 | semidirect |
| 4. #22558880 | C2 | semidirect |
| 5. #22558067 | C2 | semidirect |
| 6. #22558039 | C2 | semidirect |
| 10. #16863799 | C4 | semidirect |
| 11. #16863742 | C4 | semidirect |
| 189. C67 | #9291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22571327 | 2 |
| #22568927 | 2 |
| #22561028 | 2 |
| #22558880 | 2 |
| #22558067 | 2 |
| #22558039 | 2 |
| C67×#1517 | 2 |
| #9291 | 67 |