Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
408 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 2. C2×#17984756 | C2 | semidirect |
| 3. C4×C22⋊Dic139 | C2 | semidirect |
| 4. #380×C139 | C2 | semidirect |
| 5. C22×D556 | C4 | semidirect |
| 11. C2×C4⋊Dic139 | C4 | semidirect |
| 13. C2×(C2×D139)⋊C4 | C4 | semidirect |
| 34. C22⋊Dic139 | D4 | semidirect |
| 104. C4×C139 | #99 | semidirect |
| 115. C139 | #1964 | semidirect |
| 119. #380 | D139 | semidirect |
| 222. C4 | #17984756 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984816 | 2 |
| C2×#17984756 | 2 |
| C4×C22⋊Dic139 | 2 |
| #380×C139 | 2 |
| #1964 | 139 |