Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
478 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 154 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 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C89 |
| prime radical | C2×#127×C89 | C22 |
| 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×#1834 | C2 | semidirect |
| 3. C89×#1273 | C2 | semidirect |
| 57. #10678 | C89 | direct (N × H) |
| 63. #1834 | C2×C89 | semidirect |
| 64. #1273 | C2×C89 | semidirect |
| 65. C89 | #10678 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#1957 | 2 |
| C89×#1834 | 2 |
| C89×#1273 | 2 |
| #10678 | 89 |