Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
1222 conjugacy classes of subgroups; only the 318 normal subgroups are shown.
This group has 1222 conjugacy classes of subgroups — too many to draw. Only its 318 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C29 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C29 |
| prime radical | C29×#2867 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C29 ◁ C43×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C29×#486 | C2 | semidirect |
| 3. C29×#2862 | C2 | semidirect |
| 4. C29×#1961 | C2 | semidirect |
| 5. C4×C29×#97 | C2 | semidirect |
| 33. C4×C8×C29 | D4 | semidirect |
| 55. #33235 | C29 | direct (N × H) |
| 73. C2×#486 | C2×C29 | semidirect |
| 75. #2862 | C2×C29 | semidirect |
| 76. #1961 | C2×C29 | semidirect |
| 77. C4×#97 | C2×C29 | semidirect |
| 119. C4×C8 | D4×C29 | semidirect |
| 121. C29 | #33235 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#486 | 2 |
| C29×#2867 | 2 |
| C29×#2862 | 2 |
| C29×#1961 | 2 |
| C4×C29×#97 | 2 |
| #33235 | 29 |