Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
936 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 936 conjugacy classes of subgroups — too many to draw. Only its 206 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C89 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C89 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C89 ◁ C2×#117×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C89×#2619 | C2 | semidirect |
| 2. C89×#2073 | C2 | semidirect |
| 3. C89×#2011 | C2 | semidirect |
| 4. C89×#1999 | C2 | semidirect |
| 5. C89×#1818 | C2 | semidirect |
| 100. #32764 | C89 | direct (N × H) |
| 106. #2619 | C2×C89 | semidirect |
| 107. #2073 | C2×C89 | semidirect |
| 108. #2011 | C2×C89 | semidirect |
| 109. #1999 | C2×C89 | semidirect |
| 110. #1818 | C2×C89 | semidirect |
| 111. C89 | #32764 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#2619 | 2 |
| C89×#2073 | 2 |
| C89×#2011 | 2 |
| C89×#1999 | 2 |
| C89×#1818 | 2 |
| #32764 | 89 |