Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
348 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 125 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, prime radical, cosocle | C23×C163 | C24 |
| Fitting | #395×C163 | C2 |
| hypercenter | #395 | D163 |
| hypocenter | C163 | #2843 |
| LCS | G ▷ C23×C163 ▷ C163 | |
| UCS | C1 ◁ C23 ◁ #395 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 42. C4×Dic163 | Q8 | semidirect |
| 97. C163 | #2843 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781606 | 2 |
| #23781604 | 2 |
| #23781599 | 2 |
| #23781598 | 2 |
| #23781596 | 2 |
| #23781584 | 2 |
| #23781534 | 2 |
| #23781532 | 2 |
| #395×C163 | 2 |
| #2843 | 163 |