Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
696 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 159 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, prime radical | #392×C163 | C2 |
| hypercenter | #392 | D163 |
| hypocenter | C163 | #2392 |
| LCS | G ▷ C23×C163 ▷ C163 | |
| UCS | C1 ◁ C23 ◁ #392 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D4×Dic163 | C2 | semidirect |
| 2. C2×D4×Dic163 | C2 | semidirect |
| 3. C2×#19104691 | C2 | semidirect |
| 4. #23781597 | C2 | semidirect |
| 5. #23781590 | C2 | semidirect |
| 6. #23781588 | C2 | semidirect |
| 7. #23781579 | C2 | semidirect |
| 8. #23781579 | C2 | semidirect |
| 9. #23781516 | C2 | semidirect |
| 10. C22⋊C4×Dic163 | C2 | semidirect |
| 43. C22×Dic163 | D4 | semidirect |
| 62. C4×Dic163 | D4 | semidirect |
| 148. C163 | #2392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic163 | 2 |
| C2×#19104691 | 2 |
| #23781597 | 2 |
| #23781590 | 2 |
| #23781588 | 2 |
| #23781579 | 2 |
| #23781516 | 2 |
| C22⋊C4×Dic163 | 2 |
| #392×C163 | 2 |
| #2392 | 163 |