Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
670 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C29 | #1782 |
| commutator | C22×C4 | C22×C4×C29 |
| Frattini, cosocle | C2×#41 | C23×C29 |
| prime radical | C2×#41×C29 | C23 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C2×C4×C29 ◁ C4×#41×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 13. C29×#533 | C4 | semidirect |
| 14. C2×C29×C4⋊Q8 | C4 | semidirect |
| 15. C29×#519 | C4 | semidirect |
| 16. C29×#519 | C4 | semidirect |
| 124. #12724 | C29 | direct (N × H) |
| 182. #533 | C4×C29 | semidirect |
| 183. C2×C4⋊Q8 | C4×C29 | semidirect |
| 184. #519 | C4×C29 | semidirect |
| 185. #519 | C4×C29 | semidirect |
| 246. C29 | #12724 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3509 | 2 |
| C29×#2135 | 2 |
| C29×#2129 | 2 |
| C29×#2123 | 2 |
| C29×#1827 | 2 |
| #12724 | 29 |