Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
418 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 42 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C89 | #1343 |
| commutator | C2×C22⋊C4 | C2×C4×C89 |
| Frattini, cosocle | #379 | C22×C89 |
| prime radical | C89×#2021 | C2 |
| LCS | G ▷ C2×C22⋊C4 ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C89 ◁ C23×C89 ◁ C24×C89 ◁ #379×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C89×#1316 | C2 | semidirect |
| 3. C89×#1304 | C2 | semidirect |
| 4. #534×C89 | C4 | semidirect |
| 9. #342×C89 | C4 | semidirect |
| 147. #7394 | C89 | direct (N × H) |
| 158. #1316 | C2×C89 | semidirect |
| 159. #1304 | C2×C89 | semidirect |
| 160. C89 | #7394 | direct (N × H) |
| 161. #534 | C4×C89 | semidirect |
| 166. #342 | C4×C89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#2021 | 2 |
| C89×#1316 | 2 |
| C89×#1304 | 2 |
| #7394 | 89 |