Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
442 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 98 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 |
|---|---|---|
| 1. C89×#3236 | C2 | semidirect |
| 5. C89×#1485 | C2 | semidirect |
| 6. C89×#1470 | C2 | semidirect |
| 7. C89×#1291 | C2 | semidirect |
| 173. #10123 | C89 | direct (N × H) |
| 179. #3236 | C2×C89 | semidirect |
| 183. #1485 | C2×C89 | semidirect |
| 184. #1470 | C2×C89 | semidirect |
| 185. #1291 | C2×C89 | semidirect |
| 186. C89 | #10123 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#3236 | 2 |
| C89×#3235 | 2 |
| C89×#3142 | 2 |
| C89×#1496 | 2 |
| C89×#1485 | 2 |
| C89×#1470 | 2 |
| C89×#1291 | 2 |
| #10123 | 89 |