Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
1072 conjugacy classes of subgroups; only the 440 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 440 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C163 | D4 |
| commutator | C4 | C23×C4×C163 |
| Frattini, cosocle | C2×C4 | C24×C163 |
| prime radical | C23×D4×C163 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C163 ◁ C23×C4×C163 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C23×C8×C163 | C2 | semidirect |
| 3. C22×C4⋊C4×C163 | C2 | semidirect |
| 4. C2×#102×C163 | C2 | direct (N × H) |
| 8. C22×D4×C163 | C4 | semidirect |
| 13. C22×C8×C163 | C22 | semidirect |
| 15. C2×C4⋊C4×C163 | C22 | semidirect |
| 16. #102×C163 | C22 | direct (N × H) |
| 25. C2×D4×C163 | C2×C4 | semidirect |
| 34. C2×C8×C163 | C23 | semidirect |
| 36. C4⋊C4×C163 | C23 | semidirect |
| 48. D4×C163 | C22×C4 | semidirect |
| 61. C22×C163 | #102 | direct (N × H) |
| 71. C2×C163 | C2×#102 | direct (N × H) |
| 75. C163 | C22×#102 | direct (N × H) |
| 76. C22×#102 | C163 | direct (N × H) |
| 78. C23×C8 | C2×C163 | semidirect |
| 79. C22×C4⋊C4 | C2×C163 | semidirect |
| 80. C2×#102 | C2×C163 | direct (N × H) |
| 84. C22×D4 | C4×C163 | semidirect |
| 89. C22×C8 | C22×C163 | semidirect |
| 91. C2×C4⋊C4 | C22×C163 | semidirect |
| 92. #102 | C22×C163 | direct (N × H) |
| 101. C2×D4 | C2×C4×C163 | semidirect |
| 110. C2×C8 | C23×C163 | semidirect |
| 112. C4⋊C4 | C23×C163 | semidirect |
| 124. D4 | C22×C4×C163 | semidirect |
| 137. C22 | #102×C163 | direct (N × H) |
| 147. C2 | C2×#102×C163 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D4×C163 | 2 |
| C23×C8×C163 | 2 |
| C22×C4⋊C4×C163 | 2 |
| C2×#102×C163 | 2 |
| C22×#102 | 163 |