Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
2186 conjugacy classes of subgroups; only the 990 normal subgroups are shown.
This group has 2186 conjugacy classes of subgroups — too many to draw. Only its 990 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C89 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C89 |
| prime radical | C25×C89 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C89×#2865 | C2 | direct (N × H) |
| 3. C2×#387×C89 | C2 | semidirect |
| 4. C2×C43×C89 | C2 | semidirect |
| 9. #387×C89 | C22 | semidirect |
| 11. C43×C89 | C22 | semidirect |
| 50. C2×#2865 | C89 | direct (N × H) |
| 52. C2×C89 | #2865 | direct (N × H) |
| 54. #2865 | C2×C89 | direct (N × H) |
| 56. C2×#387 | C2×C89 | semidirect |
| 57. C2×C43 | C2×C89 | semidirect |
| 58. C89 | C2×#2865 | direct (N × H) |
| 63. #387 | C22×C89 | semidirect |
| 65. C43 | C22×C89 | semidirect |
| 105. C2 | C89×#2865 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#2865 | 2 |
| C2×#388×C89 | 2 |
| C2×#387×C89 | 2 |
| C2×C43×C89 | 2 |
| C2×#2865 | 89 |