Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
894 conjugacy classes of subgroups; only the 462 normal subgroups are shown.
This group has 894 conjugacy classes of subgroups — too many to draw. Only its 462 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C89 | C23 |
| commutator | C23 | C23×C4×C89 |
| Frattini, cosocle | C22×C4 | C24×C89 |
| socle, prime radical | C24×C89 | C22×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C89 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C89×#1840 | C2 | direct (N × H) |
| 46. C2×#1840 | C89 | direct (N × H) |
| 47. C2×C89 | #1840 | direct (N × H) |
| 51. #1840 | C2×C89 | direct (N × H) |
| 53. C89 | C2×#1840 | direct (N × H) |
| 96. C2 | C89×#1840 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#376×C89 | 2 |
| C89×#1840 | 2 |
| C2×#336×C89 | 2 |
| C2×#1840 | 89 |