Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
478 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 9. #16863799 | C4 | semidirect |
| 10. #16863775 | C4 | semidirect |
| 11. #16863748 | C4 | semidirect |
| 12. #16863746 | C4 | semidirect |
| 102. C42×C67 | Q16 | semidirect |
| 162. C67 | #9845 | semidirect |
| 257. C42 | #11761618 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570791 | 2 |
| #22561186 | 2 |
| C42×C67⋊C8 | 2 |
| #22558967 | 2 |
| #22558664 | 2 |
| #22558663 | 2 |
| C67×#1994 | 2 |
| #9845 | 67 |