Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
278 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 74 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 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C89 |
| prime radical | C23×C89 | AGL(1,ℤ/8) |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C89 ◁ C22×C4×C89 ◁ #424×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 132. #12296 | C89 | direct (N × H) |
| 144. C89 | #12296 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#3261 | 2 |
| C89×#2236 | 2 |
| C89×#2235 | 2 |
| C89×#2089 | 2 |
| C89×#1350 | 2 |
| C89×#1323 | 2 |
| #12296 | 89 |