Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
292 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 292 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 |
|---|---|---|
| 4. C2×#17984752 | C2 | semidirect |
| 5. #22580717 | C2 | semidirect |
| 6. #22580712 | C2 | semidirect |
| 7. #405×C139 | C2 | semidirect |
| 10. #17984848 | C4 | semidirect |
| 16. #17984768 | C4 | semidirect |
| 17. #17984765 | C4 | semidirect |
| 18. #17984762 | C4 | semidirect |
| 98. C139 | #1765 | semidirect |
| 103. #405 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984848 | 2 |
| C2×#17984768 | 2 |
| #22580947 | 2 |
| C2×#17984752 | 2 |
| #22580717 | 2 |
| #22580712 | 2 |
| #405×C139 | 2 |
| #1765 | 139 |