Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
464 conjugacy classes of subgroups; only the 194 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 194 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×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C29 |
| prime radical | C23×C29 | C2×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C29×#117 ◁ C29×#405 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#2229 | C2 | semidirect |
| 5. C29×#2209 | C2 | semidirect |
| 71. #33827 | C29 | direct (N × H) |
| 87. #2229 | C2×C29 | semidirect |
| 90. #2209 | C2×C29 | semidirect |
| 145. C29 | #33827 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3177 | 2 |
| C29×#2229 | 2 |
| C29×#2219 | 2 |
| C29×#2216 | 2 |
| C29×#2209 | 2 |
| C29×#2151 | 2 |
| #33827 | 29 |