Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
984 conjugacy classes of subgroups; only the 386 normal subgroups are shown.
This group has 984 conjugacy classes of subgroups — too many to draw. Only its 386 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C89 | C24 |
| commutator | C22 | C23×C8×C89 |
| Frattini, cosocle | C22×C4 | C24×C89 |
| socle | C23×C89 | C23×C4 |
| prime radical | C2×#127×C89 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C89×#1869 | C2 | semidirect |
| 3. C89×#1839 | C2 | semidirect |
| 16. #127×C89 | C8 | semidirect |
| 28. C2×D4×C89 | C2×C8 | semidirect |
| 41. C42×C89 | C2×C8 | semidirect |
| 67. #23355 | C89 | direct (N × H) |
| 73. #1869 | C2×C89 | semidirect |
| 74. #1839 | C2×C89 | semidirect |
| 75. C89 | #23355 | direct (N × H) |
| 88. #127 | C8×C89 | semidirect |
| 100. C2×D4 | C2×C8×C89 | semidirect |
| 113. C42 | C2×C8×C89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#127×C89 | 2 |
| C89×#1869 | 2 |
| C89×#1839 | 2 |
| #23355 | 89 |