Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
230 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 94 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 | #340 |
| commutator | C2×C8 | C42×C89 |
| Frattini, cosocle | C2×C4×C8 | C22×C89 |
| prime radical | C23×C89 | #102 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C89 ◁ C2×C42×C89 ◁ C2×C4×C8×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. C4⋊C16×C89 | C4 | semidirect |
| 13. #334×C89 | C4 | semidirect |
| 81. #7301 | C89 | direct (N × H) |
| 90. C89 | #7301 | direct (N × H) |
| 95. C4⋊C16 | C4×C89 | semidirect |
| 100. #334 | C4×C89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#2163 | 2 |
| C4×#107×C89 | 2 |
| C89×#1568 | 2 |
| #7301 | 89 |