Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
340 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C163 | #386 |
| commutator | C23 | C22×C4×C163 |
| Frattini, cosocle | C22×C4 | C23×C163 |
| prime radical | #535×C163 | C2 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C163 ◁ C22×C4×C163 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #568×C163 | C2 | semidirect |
| 3. #413×C163 | C2 | semidirect |
| 4. C2×#100×C163 | C2 | semidirect |
| 5. #344×C163 | C2 | semidirect |
| 37. M16×C163 | D4 | semidirect |
| 85. C163 | #1914 | direct (N × H) |
| 86. #1914 | C163 | direct (N × H) |
| 87. #568 | C2×C163 | semidirect |
| 89. #413 | C2×C163 | semidirect |
| 90. C2×#100 | C2×C163 | semidirect |
| 91. #344 | C2×C163 | semidirect |
| 123. M16 | D4×C163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #568×C163 | 2 |
| #535×C163 | 2 |
| #413×C163 | 2 |
| C2×#100×C163 | 2 |
| #344×C163 | 2 |
| #1914 | 163 |