Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
210 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C89 | #95 |
| commutator | C2×C4 | C4×C8×C89 |
| Frattini, cosocle | C2×C4×C8 | C22×C89 |
| socle | C22×C89 | #336 |
| prime radical | C23×C89 | C22⋊C8 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C89 ◁ C2×C4×C8×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 11. #346×C89 | C4 | semidirect |
| 12. C4×C16×C89 | C4 | semidirect |
| 82. #7144 | C89 | direct (N × H) |
| 90. C89 | #7144 | direct (N × H) |
| 98. #346 | C4×C89 | semidirect |
| 99. C4×C16 | C4×C89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#2163 | 2 |
| C89×#2162 | 2 |
| C89×#1746 | 2 |
| #7144 | 89 |