Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
276 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C29 | #482 |
| commutator, Frattini, cosocle | C22×C8 | C23×C29 |
| socle | C2×C29 | #2076 |
| prime radical | C2×#41×C29 | D4 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C29 ◁ C22×C4×C29 ◁ C2×C29×#131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#2158 | C2 | semidirect |
| 5. C29×#1389 | C2 | semidirect |
| 6. C29×#1384 | C2 | semidirect |
| 7. C29×#1382 | C2 | semidirect |
| 90. #13500 | C29 | direct (N × H) |
| 117. #2158 | C2×C29 | semidirect |
| 121. #1389 | C2×C29 | semidirect |
| 122. #1384 | C2×C29 | semidirect |
| 123. #1382 | C2×C29 | semidirect |
| 188. C29 | #13500 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2158 | 2 |
| C2×C29×#350 | 2 |
| C29×#1814 | 2 |
| C29×#1812 | 2 |
| C29×#1389 | 2 |
| C29×#1384 | 2 |
| C29×#1382 | 2 |
| #13500 | 29 |