Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
990 conjugacy classes of subgroups; only the 366 normal subgroups are shown.
This group has 990 conjugacy classes of subgroups — too many to draw. Only its 366 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 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C89 |
| Frattini, cosocle | C24 | C24×C89 |
| prime radical | C24×C89 | C24 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C89 ◁ C22×C4⋊C4×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C2×C4⋊Q8×C89 | C4 | semidirect |
| 7. C2×#125×C89 | C4 | semidirect |
| 94. #21828 | C89 | direct (N × H) |
| 104. C89 | #21828 | direct (N × H) |
| 106. C2×C4⋊Q8 | C4×C89 | semidirect |
| 107. C2×#125 | C4×C89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#544×C89 | 2 |
| C89×#2313 | 2 |
| C89×#1996 | 2 |
| C89×#1820 | 2 |
| #21828 | 89 |