Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
408 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 218 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C89 | #555 |
| commutator, Frattini, cosocle | C22×C4 | C24×C89 |
| socle | C2×C89 | #2571 |
| prime radical | C23×C89 | 2−1+4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C89 ◁ C22×C4×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 77. #29230 | C89 | direct (N × H) |
| 86. C89 | #29230 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#2102 | 2 |
| C89×#1953 | 2 |
| C89×#1848 | 2 |
| C89×#1833 | 2 |
| C89×#1772 | 2 |
| #29230 | 89 |