Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
324 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 101 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 |
|---|---|---|
| 11. C22×Q8×C139 | C4 | semidirect |
| 17. C2×C4⋊C4×C139 | C4 | semidirect |
| 18. C2×C4⋊C4×C139 | C4 | semidirect |
| 25. C22⋊Dic139 | Q8 | semidirect |
| 103. C139 | #1996 | semidirect |
| 109. C22×Q8 | Dic139 | semidirect |
| 116. C2×C4⋊C4 | Dic139 | semidirect |
| 117. C2×C4⋊C4 | Dic139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22580813 | 2 |
| C4×C22⋊Dic139 | 2 |
| #22580720 | 2 |
| C2×C22⋊Q8×C139 | 2 |
| #1996 | 139 |