Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
1546 conjugacy classes of subgroups; only the 446 normal subgroups are shown.
This group has 1546 conjugacy classes of subgroups — too many to draw. Only its 446 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 | C22×C22⋊C4 |
| commutator | C23 | C23×C4×C29 |
| Frattini, cosocle | C24 | C24×C29 |
| prime radical | C23×D4×C29 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C23×D4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C29×#1819 | C2 | semidirect |
| 4. C29×#1740 | C2 | semidirect |
| 7. C2×C4×D4×C29 | C4 | semidirect |
| 56. #20690 | C29 | direct (N × H) |
| 79. #1819 | C2×C29 | semidirect |
| 80. #1740 | C2×C29 | semidirect |
| 96. C2×C4×D4 | C4×C29 | semidirect |
| 126. C29 | #20690 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#518 | 2 |
| C29×#2309 | 2 |
| C29×#1819 | 2 |
| C29×#1740 | 2 |
| #20690 | 29 |