Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. #22581510 | C2 | semidirect |
| 2. #22581312 | C2 | semidirect |
| 3. #22581307 | C2 | semidirect |
| 4. #22580962 | C2 | semidirect |
| 6. C4×#14555769 | C2 | semidirect |
| 9. #17984842 | C22 | semidirect |
| 10. #17984834 | C22 | semidirect |
| 14. #17984766 | C22 | semidirect |
| 16. #17984753 | C22 | semidirect |
| 17. C4×C139⋊C8 | C22 | semidirect |
| 83. C139 | #3140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581510 | 2 |
| #22581312 | 2 |
| #22581307 | 2 |
| #22580962 | 2 |
| #22580958 | 2 |
| C4×#14555769 | 2 |
| C2×#124×C139 | 2 |
| #3140 | 139 |