Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
558 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 99. C2×C4×C89 | Q32 | semidirect |
| 140. C89 | #13330 | semidirect |
| 241. C2×C4 | #15667958 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667958 | 2 |
| C2×#19151978 | 2 |
| C2×#19151401 | 2 |
| #26018330 | 2 |
| C89×#1969 | 2 |
| #13330 | 89 |