Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
400 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 134 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 | #390 |
| commutator | C42 | C22×C4×C29 |
| Frattini, cosocle | C2×C42 | C23×C29 |
| prime radical | C29×#532 | C22 |
| LCS | G ▷ 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×#1835 | C2 | semidirect |
| 3. C29×#1518 | C2 | semidirect |
| 5. C29×#1450 | C2 | semidirect |
| 10. C29×#487 | C4 | semidirect |
| 11. C29×#486 | C4 | semidirect |
| 72. #9757 | C29 | direct (N × H) |
| 95. #1835 | C2×C29 | semidirect |
| 96. #1518 | C2×C29 | semidirect |
| 98. #1450 | C2×C29 | semidirect |
| 115. #487 | C4×C29 | semidirect |
| 116. #486 | C4×C29 | semidirect |
| 156. C29 | #9757 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3131 | 2 |
| C29×#1835 | 2 |
| C29×#1518 | 2 |
| C29×#1517 | 2 |
| C29×#1450 | 2 |
| #9757 | 29 |