Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
178 conjugacy classes of subgroups; only the 46 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C89 | #1317 |
| commutator | C24 | C2×C8×C89 |
| Frattini, cosocle | #407 | C22×C89 |
| prime radical | C24×C89 | C2×C8 |
| LCS | G ▷ C24 ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C89 ◁ C2×C4×C89 ◁ C22×C4×C89 ◁ #407×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 60. #7351 | C89 | direct (N × H) |
| 67. C89 | #7351 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C89×#1822 | 2 |
| C89×#1320 | 2 |
| #7351 | 89 |