Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
408 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 408 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 |
|---|---|---|
| 1. #22581487 | C2 | semidirect |
| 2. #22581359 | C2 | semidirect |
| 3. #22581340 | C2 | semidirect |
| 4. #22581317 | C2 | semidirect |
| 5. #22581315 | C2 | semidirect |
| 6. #22581204 | C2 | semidirect |
| 7. #22581197 | C2 | semidirect |
| 8. C4×#14555773 | C2 | semidirect |
| 9. C4×#14555770 | C2 | semidirect |
| 10. C4×#14555769 | C2 | semidirect |
| 11. #532×C139 | C2 | semidirect |
| 91. C139⋊C8 | #41 | semidirect |
| 137. C139 | #3171 | semidirect |
| 139. #532 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581487 | 2 |
| #22581359 | 2 |
| #22581340 | 2 |
| #22581317 | 2 |
| #22581315 | 2 |
| #22581204 | 2 |
| #22581197 | 2 |
| C4×#14555773 | 2 |
| C4×#14555770 | 2 |
| C4×#14555769 | 2 |
| #532×C139 | 2 |
| #3171 | 139 |