Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
996 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 230 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 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C89 |
| LCS | G ▷ 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×#3548 | C2 | semidirect |
| 2. C89×#3205 | C2 | semidirect |
| 3. C89×#3138 | C2 | semidirect |
| 4. C89×#1625 | C2 | semidirect |
| 5. C89×#1544 | C2 | semidirect |
| 6. C89×#1484 | C2 | semidirect |
| 10. #547×C89 | C22 | semidirect |
| 25. #332×C89 | C22 | semidirect |
| 26. D4⋊C8×C89 | C22 | semidirect |
| 147. #18727 | C89 | direct (N × H) |
| 153. #3548 | C2×C89 | semidirect |
| 154. #3205 | C2×C89 | semidirect |
| 155. #3138 | C2×C89 | semidirect |
| 156. #1625 | C2×C89 | semidirect |
| 157. #1544 | C2×C89 | semidirect |
| 158. #1484 | C2×C89 | semidirect |
| 159. C89 | #18727 | direct (N × H) |
| 163. #547 | C22×C89 | semidirect |
| 178. #332 | C22×C89 | semidirect |
| 179. D4⋊C8 | C22×C89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#3548 | 2 |
| C89×#3205 | 2 |
| C89×#3138 | 2 |
| C89×#1625 | 2 |
| C89×#1544 | 2 |
| C89×#1484 | 2 |
| #18727 | 89 |