Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
542 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 150 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 |
|---|---|---|
| 1. C89×#2982 | C2 | semidirect |
| 3. C89×#1801 | C2 | semidirect |
| 5. C89×#1286 | C2 | semidirect |
| 145. #9486 | C89 | direct (N × H) |
| 152. #2982 | C2×C89 | semidirect |
| 154. #1801 | C2×C89 | semidirect |
| 156. #1286 | C2×C89 | semidirect |
| 157. C89 | #9486 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#2982 | 2 |
| C89×#2536 | 2 |
| C89×#1801 | 2 |
| C89×#1486 | 2 |
| C89×#1286 | 2 |
| #9486 | 89 |