Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
932 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 932 conjugacy classes of subgroups — too many to draw. Only its 232 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C163 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C163 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C163 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#41×C163 | C2 | semidirect |
| 2. C2×#121×C163 | C2 | semidirect |
| 3. #393×C163 | C2 | semidirect |
| 4. #392×C163 | C2 | semidirect |
| 5. #380×C163 | C2 | semidirect |
| 27. C22×C4×C163 | D4 | semidirect |
| 72. C163 | #2615 | direct (N × H) |
| 73. #2615 | C163 | direct (N × H) |
| 74. C22×#41 | C2×C163 | semidirect |
| 75. C2×#121 | C2×C163 | semidirect |
| 76. #393 | C2×C163 | semidirect |
| 77. #392 | C2×C163 | semidirect |
| 78. #380 | C2×C163 | semidirect |
| 100. C22×C4 | D4×C163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#41×C163 | 2 |
| C2×#121×C163 | 2 |
| #393×C163 | 2 |
| #392×C163 | 2 |
| #380×C163 | 2 |
| #2615 | 163 |