Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
396 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22581677 | C2 | semidirect |
| 3. #22581301 | C2 | semidirect |
| 4. #22581279 | C2 | semidirect |
| 5. #22581183 | C2 | semidirect |
| 6. #22581154 | C2 | semidirect |
| 7. #22581118 | C2 | semidirect |
| 8. C4×#14555775 | C2 | semidirect |
| 9. #22581018 | C2 | semidirect |
| 10. #22580948 | C2 | semidirect |
| 11. #475×C139 | C2 | semidirect |
| 127. C139 | #3304 | semidirect |
| 133. #475 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581677 | 2 |
| #22581625 | 2 |
| #22581301 | 2 |
| #22581279 | 2 |
| #22581183 | 2 |
| #22581154 | 2 |
| #22581118 | 2 |
| C4×#14555775 | 2 |
| #22581018 | 2 |
| #22580948 | 2 |
| #475×C139 | 2 |
| #3304 | 139 |