Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
5150 conjugacy classes of subgroups; only the 3614 normal subgroups are shown.
This group has 5150 conjugacy classes of subgroups — too many to draw. Only its 3614 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24×C4×C79 | C22 |
| commutator | C2 | C23×C42×C79 |
| Frattini, cosocle | C23 | C25×C79 |
| socle, prime radical | C25×C79 | C23 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C24×C4×C79 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#376×C79 | C2 | direct (N × H) |
| 6. C22×C42×C79 | C4 | semidirect |
| 8. #376×C79 | C22 | direct (N × H) |
| 16. C2×C42×C79 | C2×C4 | semidirect |
| 29. C42×C79 | C22×C4 | semidirect |
| 40. C22×C79 | #376 | direct (N × H) |
| 47. C22×#376 | C79 | direct (N × H) |
| 48. C2×C79 | C2×#376 | direct (N × H) |
| 52. C2×#376 | C2×C79 | direct (N × H) |
| 54. C79 | C22×#376 | direct (N × H) |
| 57. C22×C42 | C4×C79 | semidirect |
| 59. #376 | C22×C79 | direct (N × H) |
| 67. C2×C42 | C2×C4×C79 | semidirect |
| 80. C42 | C22×C4×C79 | semidirect |
| 91. C22 | #376×C79 | direct (N × H) |
| 98. C2 | C2×#376×C79 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C42×C79 | 2 |
| C2×#376×C79 | 2 |
| C22×#95×C79 | 2 |
| C22×#376 | 79 |