Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
256 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C163 | C2×D4 |
| commutator | C2×C4 | C22×C4×C163 |
| Frattini, cosocle | C22×C4 | C23×C163 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C163 ◁ C2×C42×C163 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 14. #97×C163 | C4 | semidirect |
| 45. C8×C163 | C4⋊C4 | semidirect |
| 62. C163 | #1847 | direct (N × H) |
| 63. #1847 | C163 | direct (N × H) |
| 77. #97 | C4×C163 | semidirect |
| 108. C8 | C4⋊C4×C163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#107×C163 | 2 |
| C2×#106×C163 | 2 |
| C2×#97×C163 | 2 |
| #384×C163 | 2 |
| #382×C163 | 2 |
| #1847 | 163 |