Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
636 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 230 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C29 | C2×#127 |
| commutator, Frattini, cosocle | C42 | C24×C29 |
| prime radical | C23×C29 | #127 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C29×#1723 | C2 | semidirect |
| 4. C29×#1718 | C2 | semidirect |
| 62. #19711 | C29 | direct (N × H) |
| 78. #1723 | C2×C29 | semidirect |
| 79. #1718 | C2×C29 | semidirect |
| 130. C29 | #19711 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3231 | 2 |
| C29×#3170 | 2 |
| C29×#1723 | 2 |
| C29×#1718 | 2 |
| C29×#1452 | 2 |
| #19711 | 29 |