Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
490 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 214 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 ◁ C2×C42×C29 ◁ C2×C4×C8×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#2227 | C2 | semidirect |
| 4. C29×#2209 | C2 | semidirect |
| 67. #33815 | C29 | direct (N × H) |
| 77. C2×C4×C29 | Q32 | semidirect |
| 87. #2227 | C2×C29 | semidirect |
| 89. #2209 | C2×C29 | semidirect |
| 142. C29 | #33815 | direct (N × H) |
| 177. C2×C4 | C29×Q32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3170 | 2 |
| C29×#2227 | 2 |
| C29×#2216 | 2 |
| C29×#2209 | 2 |
| C2×C29×C4⋊C16 | 2 |
| #33815 | 29 |