Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
838 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 838 conjugacy classes of subgroups — too many to draw. Only its 122 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 | #386 |
| commutator | C22×C4 | C22×C4×C29 |
| Frattini, cosocle | C23×C4 | C23×C29 |
| prime radical | C29×#2404 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#2312 | C2 | semidirect |
| 3. C29×#1789 | C2 | semidirect |
| 4. C29×#1462 | C2 | semidirect |
| 5. C29×#1284 | C2 | semidirect |
| 11. C29×#393 | C4 | semidirect |
| 12. C29×#392 | C4 | semidirect |
| 45. C2×C42×C29 | D4 | semidirect |
| 104. #9479 | C29 | direct (N × H) |
| 157. #2312 | C2×C29 | semidirect |
| 158. #1789 | C2×C29 | semidirect |
| 159. #1462 | C2×C29 | semidirect |
| 160. #1284 | C2×C29 | semidirect |
| 195. #393 | C4×C29 | semidirect |
| 196. #392 | C4×C29 | semidirect |
| 237. C2×C42 | D4×C29 | semidirect |
| 246. C29 | #9479 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2404 | 2 |
| C29×#2312 | 2 |
| C29×#1789 | 2 |
| C29×#1462 | 2 |
| C29×#1284 | 2 |
| #9479 | 29 |