Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
156 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 156 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 |
|---|---|---|
| 51. Q8×C139 | Q16 | semidirect |
| 72. C139 | #1670 | semidirect |
| 119. Q8 | #14555775 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581332 | 2 |
| #22581238 | 2 |
| Q8×C139⋊C8 | 2 |
| #22580705 | 2 |
| #22580699 | 2 |
| #22580698 | 2 |
| #475×C139 | 2 |
| #1670 | 139 |