Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
944 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 163 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 | #394×C163 | C2 |
| hypercenter | #394 | D163 |
| hypocenter | C163 | #2388 |
| LCS | G ▷ C23×C163 ▷ C163 | |
| UCS | C1 ◁ C23 ◁ #394 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#14579698 | C2 | semidirect |
| 2. C2×#19104697 | C2 | semidirect |
| 3. C2×(C22⋊D163)⋊C4 | C2 | semidirect |
| 4. #23781585 | C2 | semidirect |
| 5. #23781580 | C2 | semidirect |
| 6. #23781578 | C2 | semidirect |
| 7. #23781574 | C2 | semidirect |
| 8. #23781573 | C2 | semidirect |
| 9. C22⋊C4×Dic163 | C2 | semidirect |
| 10. #23781512 | C2 | semidirect |
| 11. #394×C163 | C2 | semidirect |
| 55. C22×Dic163 | D4 | semidirect |
| 63. C2×C4×D163 | D4 | semidirect |
| 91. C22×D163 | #41 | semidirect |
| 106. C2×Dic163 | #41 | semidirect |
| 127. C2×C4×C163 | #41 | semidirect |
| 166. C163 | #2388 | semidirect |
| 173. #394 | D163 | semidirect |
| 294. C2×C4 | #14579698 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579698 | 2 |
| C2×#19104697 | 2 |
| C2×(C22⋊D163)⋊C4 | 2 |
| #23781585 | 2 |
| #23781580 | 2 |
| #23781578 | 2 |
| #23781574 | 2 |
| #23781573 | 2 |
| C22⋊C4×Dic163 | 2 |
| #23781512 | 2 |
| #394×C163 | 2 |
| #2388 | 163 |