Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
380 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 90 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 | C22×D4×C29 | D4 |
| 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 |
|---|---|---|
| 3. C29×#1569 | C2 | semidirect |
| 4. C29×#1559 | C2 | semidirect |
| 6. C29×#1526 | C2 | semidirect |
| 7. C29×#1291 | C2 | semidirect |
| 122. #10498 | C29 | direct (N × H) |
| 160. #1569 | C2×C29 | semidirect |
| 161. #1559 | C2×C29 | semidirect |
| 163. #1526 | C2×C29 | semidirect |
| 164. #1291 | C2×C29 | semidirect |
| 255. C29 | #10498 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3215 | 2 |
| C29×#1967 | 2 |
| C29×#1569 | 2 |
| C29×#1559 | 2 |
| C29×#1527 | 2 |
| C29×#1526 | 2 |
| C29×#1291 | 2 |
| #10498 | 29 |