Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
516 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C89 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C89 |
| prime radical | #532×C89 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C89 ◁ C2×C42×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C89×#3255 | C2 | semidirect |
| 3. C89×#1994 | C2 | semidirect |
| 5. C89×#1309 | C2 | semidirect |
| 129. #10302 | C89 | direct (N × H) |
| 134. #3255 | C2×C89 | semidirect |
| 136. #1994 | C2×C89 | semidirect |
| 138. #1309 | C2×C89 | semidirect |
| 139. C89 | #10302 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#3255 | 2 |
| C89×#3254 | 2 |
| C89×#1994 | 2 |
| C89×#1962 | 2 |
| C89×#1309 | 2 |
| #10302 | 89 |