Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
162 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C89 | #357 |
| commutator | C16 | C42×C89 |
| Frattini, cosocle | C22×C16 | C22×C89 |
| socle | C2×C89 | #1380 |
| prime radical | C23×C89 | Q32 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C89 ◁ C22×C4×C89 ◁ C22×C8×C89 ◁ C22×C16×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 66. #7479 | C89 | direct (N × H) |
| 74. C89 | #7479 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M64×C89 | 2 |
| C2×#368×C89 | 2 |
| #7479 | 89 |