Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
736 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C163 | C23 |
| commutator | C23 | C22×C4×C163 |
| Frattini, cosocle | C24 | C23×C163 |
| prime radical | C25×C163 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C163 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#95×C163 | C2 | semidirect |
| 10. C2×C22⋊C4×C163 | C4 | semidirect |
| 84. C163 | #1440 | direct (N × H) |
| 85. #1440 | C163 | direct (N × H) |
| 88. C2×#95 | C2×C163 | semidirect |
| 95. C2×C22⋊C4 | C4×C163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊C4×C163 | 2 |
| C2×#95×C163 | 2 |
| #1440 | 163 |