Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
560 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 102 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 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C89 |
| prime radical | #532×C89 | C22 |
| LCS | G ▷ C2×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 |
|---|---|---|
| 3. C89×#2660 | C2 | semidirect |
| 4. C89×#1558 | C2 | semidirect |
| 5. C89×#1528 | C2 | semidirect |
| 7. C89×#1300 | C2 | semidirect |
| 171. #10091 | C89 | direct (N × H) |
| 179. #2660 | C2×C89 | semidirect |
| 180. #1558 | C2×C89 | semidirect |
| 181. #1528 | C2×C89 | semidirect |
| 183. #1300 | C2×C89 | semidirect |
| 184. C89 | #10091 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#3234 | 2 |
| C89×#3152 | 2 |
| C89×#2660 | 2 |
| C89×#1558 | 2 |
| C89×#1528 | 2 |
| C89×#1505 | 2 |
| C89×#1300 | 2 |
| #10091 | 89 |