Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
630 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 146 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C89 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C89 |
| prime radical | C89×#2537 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C89 ◁ C2×C42×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C89×#1845 | C2 | semidirect |
| 3. C89×#1802 | C2 | semidirect |
| 4. C2×D4⋊C8×C89 | C2 | semidirect |
| 5. C89×#1296 | C2 | semidirect |
| 42. C4×C8×C89 | D4 | semidirect |
| 141. #10430 | C89 | direct (N × H) |
| 149. #1845 | C2×C89 | semidirect |
| 150. #1802 | C2×C89 | semidirect |
| 151. C2×D4⋊C8 | C2×C89 | semidirect |
| 152. #1296 | C2×C89 | semidirect |
| 153. C89 | #10430 | direct (N × H) |
| 190. C4×C8 | D4×C89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#2537 | 2 |
| C89×#1845 | 2 |
| C89×#1802 | 2 |
| C2×D4⋊C8×C89 | 2 |
| C89×#1296 | 2 |
| #10430 | 89 |