Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
116 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 39 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 |
|---|---|---|
| 4. C2×Dic556 | C4 | semidirect |
| 7. #17984776 | C4 | semidirect |
| 54. C139 | #1348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22581194 | 2 |
| C22⋊(C139⋊C16) | 2 |
| #340×C139 | 2 |
| #1348 | 139 |