Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
362 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22581663 | C2 | semidirect |
| 2. #22581307 | C2 | semidirect |
| 3. #22581299 | C2 | semidirect |
| 4. #22581253 | C2 | semidirect |
| 5. #22581248 | C2 | semidirect |
| 6. #22581165 | C2 | semidirect |
| 8. Q8×C139⋊C8 | C2 | semidirect |
| 9. C4×#14555772 | C2 | semidirect |
| 10. C4×#14555770 | C2 | semidirect |
| 11. #559×C139 | C2 | semidirect |
| 122. C139 | #3361 | semidirect |
| 124. #559 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581663 | 2 |
| #22581307 | 2 |
| #22581299 | 2 |
| #22581253 | 2 |
| #22581248 | 2 |
| #22581165 | 2 |
| #22581145 | 2 |
| Q8×C139⋊C8 | 2 |
| C4×#14555772 | 2 |
| C4×#14555770 | 2 |
| #559×C139 | 2 |
| #3361 | 139 |