Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1742 conjugacy classes of subgroups; only the 579 normal subgroups are shown.
This group has 1742 conjugacy classes of subgroups — too many to draw. Only its 579 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D89 |
| commutator, socle, cosocle | C23×C89 | C25 |
| Fitting | C89×#2845 | C2 |
| prime radical | C23×D89 | C24 |
| hypercenter | #2845 | D89 |
| hypocenter | C89 | C2×#2845 |
| LCS | G ▷ C23×C89 ▷ C89 | |
| UCS | C1 ◁ C23 ◁ #2845 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26028527 | C2 | semidirect |
| 2. #26028526 | C2 | semidirect |
| 5. C89×#2845 | C2 | semidirect |
| 95. D89 | #2845 | direct (N × H) |
| 98. #2845 | D89 | direct (N × H) |
| 101. C89 | C2×#2845 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028527 | 2 |
| #26028526 | 2 |
| #398×D89 | 2 |
| #382×D89 | 2 |
| C89×#2845 | 2 |
| C2×#2845 | 89 |