Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
414 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 94 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 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C29 |
| prime radical | C29×#3213 | C2 |
| LCS | G ▷ C2×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×#1983 | C2 | semidirect |
| 3. C29×#1573 | C2 | semidirect |
| 4. C29×#1551 | C2 | semidirect |
| 5. C29×#1502 | C2 | semidirect |
| 6. C29×#1469 | C2 | semidirect |
| 7. C29×#1285 | C2 | semidirect |
| 120. #10508 | C29 | direct (N × H) |
| 165. #1983 | C2×C29 | semidirect |
| 166. #1573 | C2×C29 | semidirect |
| 167. #1551 | C2×C29 | semidirect |
| 168. #1502 | C2×C29 | semidirect |
| 169. #1469 | C2×C29 | semidirect |
| 170. #1285 | C2×C29 | semidirect |
| 265. C29 | #10508 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3213 | 2 |
| C29×#1983 | 2 |
| C29×#1573 | 2 |
| C29×#1551 | 2 |
| C29×#1502 | 2 |
| C29×#1469 | 2 |
| C29×#1285 | 2 |
| #10508 | 29 |