Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
146 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 46. C139⋊C8 | Q16 | semidirect |
| 70. C139 | #1692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581349 | 2 |
| #22581163 | 2 |
| #22581084 | 2 |
| #22580705 | 2 |
| #22580702 | 2 |
| #22580700 | 2 |
| #477×C139 | 2 |
| #1692 | 139 |