Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
2078 conjugacy classes of subgroups; only the 987 normal subgroups are shown.
This group has 2078 conjugacy classes of subgroups — too many to draw. Only its 987 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D89 |
| commutator | C2×C89 | C2×C43 |
| Fitting | C2×#376×C89 | C2 |
| socle, prime radical, cosocle | C24×C89 | C24 |
| hypercenter | C2×#376 | D89 |
| hypocenter | C89 | #13750 |
| LCS | G ▷ C2×C89 ▷ C89 | |
| UCS | C1 ◁ C24 ◁ C2×#376 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C4×C4⋊Dic89 | C4 | semidirect |
| 9. #376×C89 | C4 | semidirect |
| 24. C4⋊Dic89 | C42 | semidirect |
| 34. C42×C89 | C42 | semidirect |
| 66. C89 | #13750 | semidirect |
| 71. #376 | Dic89 | semidirect |
| 97. C42 | C4×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C4⋊Dic89 | 2 |
| #95×Dic89 | 2 |
| C2×#376×C89 | 2 |
| #13750 | 89 |