Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
360 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 360 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×#532 | C22 |
| 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×#1989 | C2 | semidirect |
| 3. C29×#1573 | C2 | semidirect |
| 6. C29×#1470 | C2 | semidirect |
| 7. C29×#1285 | C2 | semidirect |
| 109. #10509 | C29 | direct (N × H) |
| 146. #1989 | C2×C29 | semidirect |
| 147. #1573 | C2×C29 | semidirect |
| 150. #1470 | C2×C29 | semidirect |
| 151. #1285 | C2×C29 | semidirect |
| 239. C29 | #10509 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3234 | 2 |
| C29×#1989 | 2 |
| C29×#1573 | 2 |
| C29×#1551 | 2 |
| C29×#1502 | 2 |
| C29×#1470 | 2 |
| C29×#1285 | 2 |
| #10509 | 29 |