Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
456 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 456 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. #22560234 | C2 | semidirect |
| 4. #22558116 | C2 | semidirect |
| 5. C67×#1810 | C2 | semidirect |
| 6. C2×#14524049 | C4 | semidirect |
| 13. #16863422 | C4 | semidirect |
| 14. #16863362 | C4 | semidirect |
| 16. #16863351 | C4 | semidirect |
| 186. #1810 | D67 | semidirect |
| 190. C67 | #8626 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22568903 | 2 |
| #22560234 | 2 |
| #22558753 | 2 |
| #22558116 | 2 |
| C67×#1810 | 2 |
| #8626 | 67 |