Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
342 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 122 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 | C2×D8 |
| commutator, Frattini, cosocle | C22×C8 | C23×C29 |
| prime radical | C24×C29 | D8 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C29 ◁ C23×C4×C29 ◁ C23×C8×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C29×#366 | C2 | semidirect |
| 4. C29×#1380 | C2 | semidirect |
| 5. C29×#1380 | C2 | semidirect |
| 59. #13492 | C29 | direct (N × H) |
| 85. C2×#366 | C2×C29 | semidirect |
| 88. #1380 | C2×C29 | semidirect |
| 89. #1380 | C2×C29 | semidirect |
| 140. C29 | #13492 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#366 | 2 |
| C2×C29×C22⋊C16 | 2 |
| C29×#1808 | 2 |
| C29×#1380 | 2 |
| #13492 | 29 |