Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
820 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 142 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 | #379 |
| commutator | C42 | C22×C4×C29 |
| Frattini, cosocle | C2×C42 | C23×C29 |
| prime radical | C29×#3549 | C2 |
| 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×#1963 | C2 | semidirect |
| 3. C29×#1557 | C2 | semidirect |
| 4. C29×#1536 | C2 | semidirect |
| 5. C29×#1505 | C2 | semidirect |
| 8. C29×#555 | C4 | semidirect |
| 10. D42×C29 | C4 | semidirect |
| 15. C29×#432 | C22 | semidirect |
| 16. C29×#423 | C22 | semidirect |
| 18. C29×#376 | C22 | semidirect |
| 99. #8491 | C29 | direct (N × H) |
| 134. #1963 | C2×C29 | semidirect |
| 135. #1557 | C2×C29 | semidirect |
| 136. #1536 | C2×C29 | semidirect |
| 137. #1505 | C2×C29 | semidirect |
| 157. #555 | C4×C29 | semidirect |
| 159. D42 | C4×C29 | semidirect |
| 164. #432 | C22×C29 | semidirect |
| 165. #423 | C22×C29 | semidirect |
| 167. #376 | C22×C29 | semidirect |
| 213. C29 | #8491 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3549 | 2 |
| C29×#1963 | 2 |
| C29×#1557 | 2 |
| C29×#1536 | 2 |
| C29×#1505 | 2 |
| #8491 | 29 |