Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
630 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 630 conjugacy classes of subgroups — too many to draw. Only its 184 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. C2×#127×C163 | C2 | semidirect |
| 2. C2×#126×C163 | C2 | semidirect |
| 3. #394×C163 | C2 | semidirect |
| 4. #392×C163 | C2 | semidirect |
| 5. #383×C163 | C2 | semidirect |
| 26. C42×C163 | D4 | semidirect |
| 54. C163 | #2818 | direct (N × H) |
| 55. #2818 | C163 | direct (N × H) |
| 56. C2×#127 | C2×C163 | semidirect |
| 57. C2×#126 | C2×C163 | semidirect |
| 58. #394 | C2×C163 | semidirect |
| 59. #392 | C2×C163 | semidirect |
| 60. #383 | C2×C163 | semidirect |
| 81. C42 | D4×C163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#127×C163 | 2 |
| C2×#126×C163 | 2 |
| #394×C163 | 2 |
| #392×C163 | 2 |
| #383×C163 | 2 |
| #2818 | 163 |