Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
174 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 102 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 | #367 |
| commutator | C16 | C42×C89 |
| Frattini, cosocle | C22×C16 | C22×C89 |
| prime radical | C23×C89 | SD32 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C89 ◁ C22×C4×C89 ◁ C22×C8×C89 ◁ C22×C16×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. C2×C32×C89 | C4 | semidirect |
| 11. #368×C89 | C4 | semidirect |
| 68. #7474 | C89 | direct (N × H) |
| 76. C89 | #7474 | direct (N × H) |
| 82. C2×C32 | C4×C89 | semidirect |
| 84. #368 | C4×C89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M64×C89 | 2 |
| C2×#368×C89 | 2 |
| C2×#367×C89 | 2 |
| #7474 | 89 |