Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
350 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 350 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 | C22×D8×C89 | C22 |
| 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 |
|---|---|---|
| 1. C89×#3261 | C2 | semidirect |
| 4. C89×#1350 | C2 | semidirect |
| 5. C89×#1323 | C2 | semidirect |
| 108. #12165 | C89 | direct (N × H) |
| 113. #3261 | C2×C89 | semidirect |
| 116. #1350 | C2×C89 | semidirect |
| 117. #1323 | C2×C89 | semidirect |
| 118. C89 | #12165 | 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×#2187 | 2 |
| C89×#2045 | 2 |
| C89×#1350 | 2 |
| C89×#1323 | 2 |
| #12165 | 89 |