Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1182 conjugacy classes of subgroups; only the 462 normal subgroups are shown.
This group has 1182 conjugacy classes of subgroups — too many to draw. Only its 462 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C79 | C24 |
| commutator | C23 | C23×C4×C79 |
| Frattini, cosocle | C24 | C24×C79 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C79 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 11. #383×C79 | C4 | semidirect |
| 50. C42×C79 | C4⋊C4 | semidirect |
| 84. #14678 | C79 | direct (N × H) |
| 95. C79 | #14678 | direct (N × H) |
| 101. #383 | C4×C79 | semidirect |
| 140. C42 | C4⋊C4×C79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#384×C79 | 2 |
| C2×#383×C79 | 2 |
| C79×#1444 | 2 |
| C79×#1442 | 2 |
| #14678 | 79 |