Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
398 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 398 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. #22581608 | C2 | semidirect |
| 2. #22581305 | C2 | semidirect |
| 3. #22581294 | C2 | semidirect |
| 4. #22581240 | C2 | semidirect |
| 5. #22581180 | C2 | semidirect |
| 6. #22581158 | C2 | semidirect |
| 7. #22581096 | C2 | semidirect |
| 8. C4×#14555770 | C2 | semidirect |
| 9. D4×C139⋊C8 | C2 | semidirect |
| 10. #22580947 | C2 | semidirect |
| 11. #555×C139 | C2 | semidirect |
| 130. C139 | #3303 | semidirect |
| 132. #555 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581608 | 2 |
| #22581305 | 2 |
| #22581294 | 2 |
| #22581240 | 2 |
| #22581180 | 2 |
| #22581158 | 2 |
| #22581096 | 2 |
| C4×#14555770 | 2 |
| D4×C139⋊C8 | 2 |
| #22580947 | 2 |
| #555×C139 | 2 |
| #3303 | 139 |