Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
200 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C29 | C2×D16 |
| commutator, Frattini, cosocle | C2×C16 | C23×C29 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C42×C29 ◁ C4×C8×C29 ◁ C4×C16×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 50. #13688 | C29 | direct (N × H) |
| 74. C4×C29 | Q64 | semidirect |
| 106. C29 | #13688 | direct (N × H) |
| 143. C4 | C29×Q64 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×Q64 | 2 |
| C29×#2247 | 2 |
| C4×C29×Q32 | 2 |
| C29×C4⋊C32 | 2 |
| C29×#1416 | 2 |
| #13688 | 29 |