Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
344 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 117 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. #22580716 | C2 | semidirect |
| 8. C2×C4⋊Dic139 | C4 | semidirect |
| 76. C139 | #1823 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Dic139 | 2 |
| #22580813 | 2 |
| #22580716 | 2 |
| C2×C22⋊C8×C139 | 2 |
| #1823 | 139 |