Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
1812 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 1812 conjugacy classes of subgroups — too many to draw. Only its 285 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D163 |
| commutator, cosocle | C23×C163 | C24 |
| Frattini | C23 | C23×D163 |
| Fitting | C23×D4×C163 | C2 |
| socle | C24×C163 | C23 |
| hypercenter | C23×D4 | D163 |
| hypocenter | C163 | C2×#392 |
| LCS | G ▷ C23×C163 ▷ C163 | |
| UCS | C1 ◁ C24 ◁ C23×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×C22⋊D163 | C2 | semidirect |
| 2. C22×C22⋊Dic163 | C2 | semidirect |
| 3. C22×(C2×D163)⋊C4 | C2 | semidirect |
| 4. #23781573 | C2 | direct (N × H) |
| 5. C2×C163⋊#95 | C2 | semidirect |
| 6. C23×D4×C163 | C2 | semidirect |
| 11. C22×C22⋊D163 | C22 | semidirect |
| 15. C2×C22⋊Dic163 | C22 | semidirect |
| 17. C2×(C2×D163)⋊C4 | C22 | semidirect |
| 18. C163⋊#95 | C22 | semidirect |
| 22. C22×D4×C163 | C22 | semidirect |
| 28. C23×D163 | D4 | semidirect |
| 38. C22×Dic163 | D4 | semidirect |
| 49. C24×C163 | D4 | semidirect |
| 56. C22×C4×C163 | D4 | semidirect |
| 67. C22×D163 | C2×D4 | semidirect |
| 75. C2×Dic163 | C2×D4 | semidirect |
| 93. C23×C163 | C2×D4 | semidirect |
| 99. C2×C4×C163 | C2×D4 | semidirect |
| 128. C2×C163 | #392 | semidirect |
| 135. C163 | C2×#392 | semidirect |
| 138. C23×D4 | D163 | semidirect |
| 151. C22×D4 | C2×D163 | semidirect |
| 172. C24 | C22⋊D163 | semidirect |
| 190. C22×C4 | C22⋊D163 | semidirect |
| 221. C23 | C2×C22⋊D163 | semidirect |
| 235. C2×C4 | C2×C22⋊D163 | semidirect |
| 265. C2 | #23781573 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊D163 | 2 |
| C22×C22⋊Dic163 | 2 |
| C22×(C2×D163)⋊C4 | 2 |
| #23781573 | 2 |
| C2×C163⋊#95 | 2 |
| C23×D4×C163 | 2 |
| C2×#392 | 163 |