Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
1718 conjugacy classes of subgroups; only the 238 normal subgroups are shown.
This group has 1718 conjugacy classes of subgroups — too many to draw. Only its 238 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×C29 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C29 |
| Frattini, cosocle | C2×C42 | C23×C29 |
| prime radical | C22×C29×#127 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C29 ◁ C22×C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#1797 | C2 | semidirect |
| 3. C2×C29×#331 | C2 | semidirect |
| 11. C2×C29×C4⋊C8 | C22 | semidirect |
| 81. #8339 | C29 | direct (N × H) |
| 122. #1797 | C2×C29 | semidirect |
| 123. C2×#331 | C2×C29 | semidirect |
| 134. C22×C29 | #331 | semidirect |
| 152. C2×C4⋊C8 | C22×C29 | semidirect |
| 188. C29 | #8339 | direct (N × H) |
| 279. C22 | C29×#331 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C29×#127 | 2 |
| C29×#1797 | 2 |
| C2×C29×#331 | 2 |
| #8339 | 29 |