Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
208 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 46 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 | #354 |
| commutator | C2×C42 | C2×C4×C89 |
| Frattini, cosocle | #390 | C22×C89 |
| prime radical | C22×D4×C89 | D4 |
| LCS | G ▷ C2×C42 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C89 ◁ C23×C89 ◁ C22×C4×C89 ◁ #390×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. #382×C89 | C4 | semidirect |
| 9. #336×C89 | C4 | semidirect |
| 91. #7412 | C89 | direct (N × H) |
| 102. C89 | #7412 | direct (N × H) |
| 106. #382 | C4×C89 | semidirect |
| 108. #336 | C4×C89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#2073 | 2 |
| C89×#1393 | 2 |
| C89×#1318 | 2 |
| #7412 | 89 |