Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
684 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 126 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 | #386 |
| commutator | C24 | C22×C4×C29 |
| Frattini, cosocle | C23×C4 | C23×C29 |
| prime radical | C22×D4×C29 | C2×C4 |
| LCS | G ▷ C24 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C29×#1784 | C2 | semidirect |
| 5. C29×#1305 | C2 | semidirect |
| 100. #9505 | C29 | direct (N × H) |
| 109. C23×C29 | #101 | semidirect |
| 144. #1784 | C2×C29 | semidirect |
| 146. #1305 | C2×C29 | semidirect |
| 228. C29 | #9505 | direct (N × H) |
| 280. C23 | C29×#101 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2973 | 2 |
| C29×#2409 | 2 |
| C29×#1784 | 2 |
| C29×#1465 | 2 |
| C29×#1305 | 2 |
| #9505 | 29 |