Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
572 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 150 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 | #120 |
| commutator | C22×C4 | C22×C4×C89 |
| Frattini, cosocle | C23×C4 | C23×C89 |
| prime radical | C24×C89 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C89 ◁ C23×C4×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 10. #400×C89 | C4 | semidirect |
| 134. #9022 | C89 | direct (N × H) |
| 147. C89 | #9022 | direct (N × H) |
| 152. #400 | C4×C89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#400×C89 | 2 |
| C89×#2313 | 2 |
| C89×#1824 | 2 |
| C2×#324×C89 | 2 |
| C89×#1294 | 2 |
| #9022 | 89 |