Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
840 conjugacy classes of subgroups; only the 222 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 222 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×#120 |
| commutator, Frattini, cosocle | C42 | C24×C29 |
| prime radical | C29×#532 | C22 |
| 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 |
|---|---|---|
| 2. C29×#3237 | C2 | semidirect |
| 4. C29×#1664 | C2 | semidirect |
| 6. C29×#1531 | C2 | semidirect |
| 114. #19058 | C29 | direct (N × H) |
| 140. #3237 | C2×C29 | semidirect |
| 142. #1664 | C2×C29 | semidirect |
| 144. #1531 | C2×C29 | semidirect |
| 230. C29 | #19058 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3550 | 2 |
| C29×#3237 | 2 |
| C29×#3135 | 2 |
| C29×#1664 | 2 |
| C29×#1536 | 2 |
| C29×#1531 | 2 |
| #19058 | 29 |