Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1110 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 1110 conjugacy classes of subgroups — too many to draw. Only its 222 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C89 | #381 |
| commutator | C24 | C22×C4×C89 |
| Frattini, cosocle | C25 | C23×C89 |
| prime radical | C23×D4×C89 | C22 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C89 ◁ C25×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#342×C89 | C2 | semidirect |
| 10. #381×C89 | C4 | semidirect |
| 11. #379×C89 | C4 | semidirect |
| 128. #11169 | C89 | direct (N × H) |
| 138. C2×#342 | C2×C89 | semidirect |
| 139. C89 | #11169 | direct (N × H) |
| 146. #381 | C4×C89 | semidirect |
| 147. #379 | C4×C89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#99×C89 | 2 |
| C89×#2308 | 2 |
| C2×#342×C89 | 2 |
| #11169 | 89 |