Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
478 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 134 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 | #390 |
| commutator | C42 | C22×C4×C89 |
| Frattini, cosocle | C2×C42 | C23×C89 |
| prime radical | C89×#3147 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C89 ◁ C2×C42×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C89×#1835 | C2 | semidirect |
| 3. C89×#1517 | C2 | semidirect |
| 4. C89×#1452 | C2 | semidirect |
| 8. #494×C89 | C4 | semidirect |
| 9. #493×C89 | C4 | semidirect |
| 10. #492×C89 | C4 | semidirect |
| 89. #9760 | C89 | direct (N × H) |
| 95. #1835 | C2×C89 | semidirect |
| 96. #1517 | C2×C89 | semidirect |
| 97. #1452 | C2×C89 | semidirect |
| 98. C89 | #9760 | direct (N × H) |
| 102. #494 | C4×C89 | semidirect |
| 103. #493 | C4×C89 | semidirect |
| 104. #492 | C4×C89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#3147 | 2 |
| C89×#1835 | 2 |
| C89×#1517 | 2 |
| C89×#1452 | 2 |
| #9760 | 89 |