Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
348 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 348 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 |
|---|---|---|
| 2. #22581310 | C2 | semidirect |
| 4. #22581250 | C2 | semidirect |
| 5. #22581235 | C2 | semidirect |
| 6. #22581175 | C2 | semidirect |
| 8. Q8×C139⋊C8 | C2 | semidirect |
| 9. C4×#14555775 | C2 | semidirect |
| 10. C4×#14555772 | C2 | semidirect |
| 11. #557×C139 | C2 | semidirect |
| 117. C139 | #3365 | semidirect |
| 120. #557 | D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581688 | 2 |
| #22581310 | 2 |
| #22581301 | 2 |
| #22581250 | 2 |
| #22581235 | 2 |
| #22581175 | 2 |
| #22581153 | 2 |
| Q8×C139⋊C8 | 2 |
| C4×#14555775 | 2 |
| C4×#14555772 | 2 |
| #557×C139 | 2 |
| #3365 | 139 |