Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
518 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 518 conjugacy classes of subgroups — too many to draw. Only its 126 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 | #386 |
| commutator | C22×C4 | C22×C4×C89 |
| Frattini, cosocle | C2×C42 | C23×C89 |
| prime radical | C22×D4×C89 | C2×C4 |
| LCS | G ▷ C22×C4 ▷ 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 |
|---|---|---|
| 3. C89×#1558 | C2 | semidirect |
| 5. C89×#1285 | C2 | semidirect |
| 152. #9451 | C89 | direct (N × H) |
| 162. #1558 | C2×C89 | semidirect |
| 164. #1285 | C2×C89 | semidirect |
| 165. C89 | #9451 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#2973 | 2 |
| C89×#2547 | 2 |
| C89×#1558 | 2 |
| C89×#1466 | 2 |
| C89×#1285 | 2 |
| #9451 | 89 |