Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
486 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 122 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×#2983 | C2 | semidirect |
| 4. C89×#1467 | C2 | semidirect |
| 5. C89×#1285 | C2 | semidirect |
| 170. #9448 | C89 | direct (N × H) |
| 177. #2983 | C2×C89 | semidirect |
| 180. #1467 | C2×C89 | semidirect |
| 181. #1285 | C2×C89 | semidirect |
| 182. C89 | #9448 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#2983 | 2 |
| C89×#2545 | 2 |
| C89×#1533 | 2 |
| C89×#1467 | 2 |
| C89×#1285 | 2 |
| #9448 | 89 |