Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
358 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C89 | C2×D8 |
| commutator, Frattini, cosocle | C22×C8 | C23×C89 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C89 ◁ C2×C42×C89 ◁ C2×C4×C8×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 103. #13531 | C89 | direct (N × H) |
| 114. C89 | #13531 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#367×C89 | 2 |
| C2×#358×C89 | 2 |
| C89×#1969 | 2 |
| C89×#1845 | 2 |
| C89×#1374 | 2 |
| #13531 | 89 |