Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 3. Q8×C139⋊C8 | C2 | semidirect |
| 4. #22580703 | C2 | semidirect |
| 5. #22580699 | C2 | semidirect |
| 7. #475×C139 | C2 | semidirect |
| 51. C139⋊C8 | SD16 | semidirect |
| 55. Q8×C139 | SD16 | semidirect |
| 79. C139 | #1666 | semidirect |
| 82. #475 | D139 | semidirect |
| 126. Q8 | #14555772 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581327 | 2 |
| #22581153 | 2 |
| Q8×C139⋊C8 | 2 |
| #22580703 | 2 |
| #22580699 | 2 |
| #22580696 | 2 |
| #475×C139 | 2 |
| #1666 | 139 |