Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
1224 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 1224 conjugacy classes of subgroups — too many to draw. Only its 209 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D163 |
| commutator, socle, cosocle | C23×C163 | C24 |
| Fitting | C2×#120×C163 | C2 |
| hypercenter | C2×#120 | D163 |
| hypocenter | C163 | #2847 |
| LCS | G ▷ C23×C163 ▷ C163 | |
| UCS | C1 ◁ C23 ◁ C2×#120 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C24×Dic163 | C2 | semidirect |
| 2. C2×#19104707 | C2 | semidirect |
| 3. C2×#19104704 | C2 | semidirect |
| 4. #23781545 | C2 | semidirect |
| 5. #23781542 | C2 | semidirect |
| 6. #23781523 | C2 | semidirect |
| 7. C2×#120×C163 | C2 | semidirect |
| 9. C22×C22⋊D163 | C22 | semidirect |
| 15. C2×Dic163⋊C4 | C22 | semidirect |
| 17. C2×C22⋊Dic163 | C22 | semidirect |
| 18. C2×(C2×D163)⋊C4 | C22 | semidirect |
| 19. C163⋊#95 | C22 | semidirect |
| 33. C22×Dic163 | D4 | semidirect |
| 43. C24×C163 | D4 | semidirect |
| 88. C22×C163 | #121 | semidirect |
| 98. Dic163 | #120 | semidirect |
| 105. C163 | #2847 | semidirect |
| 110. C2×#120 | D163 | semidirect |
| 133. C24 | C22⋊D163 | semidirect |
| 197. C22 | #19104707 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×Dic163 | 2 |
| C2×#19104707 | 2 |
| C2×#19104704 | 2 |
| #23781545 | 2 |
| #23781542 | 2 |
| #23781523 | 2 |
| C2×#120×C163 | 2 |
| #2847 | 163 |