Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
620 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C89 | #1304 |
| commutator | C22×C4 | C42×C89 |
| Frattini, cosocle | C23×D4 | C22×C89 |
| prime radical | C23×D4×C89 | C22 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C89 ◁ C23×C89 ◁ C23×D4×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C2×#99×C89 | C4 | semidirect |
| 7. #407×C89 | C4 | semidirect |
| 102. #7314 | C89 | direct (N × H) |
| 111. C89 | #7314 | direct (N × H) |
| 115. C2×#99 | C4×C89 | semidirect |
| 116. #407 | C4×C89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#1783 | 2 |
| C89×#1781 | 2 |
| #7314 | 89 |