Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
464 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 464 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 | #394 |
| commutator, Frattini, cosocle | C23×C4 | C23×C89 |
| prime radical | C2×#121×C89 | C22 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C89 ◁ C23×C4×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C89×#1901 | C2 | semidirect |
| 4. C89×#1855 | C2 | semidirect |
| 5. C89×#1520 | C2 | semidirect |
| 7. C89×#1305 | C2 | semidirect |
| 205. #10561 | C89 | direct (N × H) |
| 215. #1901 | C2×C89 | semidirect |
| 217. #1855 | C2×C89 | semidirect |
| 218. #1520 | C2×C89 | semidirect |
| 220. #1305 | C2×C89 | semidirect |
| 221. C89 | #10561 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#3193 | 2 |
| C89×#1901 | 2 |
| C89×#1895 | 2 |
| C89×#1855 | 2 |
| C89×#1520 | 2 |
| C89×#1471 | 2 |
| C89×#1305 | 2 |
| #10561 | 89 |