Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
412 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C89 | #99 |
| commutator | C22×C4 | C2×C8×C89 |
| Frattini, cosocle | C2×#95 | C22×C89 |
| prime radical | C24×C89 | C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C89 ◁ C24×C89 ◁ C2×#95×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 31. #95×C89 | C8 | semidirect |
| 154. #7123 | C89 | direct (N × H) |
| 169. C89 | #7123 | direct (N × H) |
| 197. #95 | C8×C89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#1444 | 2 |
| C89×#1280 | 2 |
| #7123 | 89 |