Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
334 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 334 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 | #353 |
| commutator | C2×C42 | C2×C4×C89 |
| Frattini, cosocle | #390 | C22×C89 |
| prime radical | C89×#2011 | C2 |
| 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 |
|---|---|---|
| 2. C89×#1393 | C2 | semidirect |
| 3. C89×#1318 | C2 | semidirect |
| 5. C2×#127×C89 | C4 | semidirect |
| 9. #336×C89 | C4 | semidirect |
| 117. #7402 | C89 | direct (N × H) |
| 127. #1393 | C2×C89 | semidirect |
| 128. #1318 | C2×C89 | semidirect |
| 129. C89 | #7402 | direct (N × H) |
| 131. C2×#127 | C4×C89 | semidirect |
| 135. #336 | C4×C89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#2011 | 2 |
| C89×#1393 | 2 |
| C89×#1318 | 2 |
| #7402 | 89 |