Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
220 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 220 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 | C22×C4×C89 | C22⋊C4 |
| commutator | C2×C4 | C2×C16×C89 |
| Frattini, cosocle | C2×C4×C8 | C22×C89 |
| socle, prime radical | C23×C89 | C22⋊C8 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C89 ◁ C2×C4×C8×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 47. C4⋊C4×C89 | C16 | semidirect |
| 95. #7118 | C89 | direct (N × H) |
| 106. C89 | #7118 | direct (N × H) |
| 150. C4⋊C4 | C16×C89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#1939 | 2 |
| C89×#1374 | 2 |
| #7118 | 89 |