Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
694 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 694 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 | C29×#535 | C22 |
| 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 |
|---|---|---|
| 4. C29×#2123 | C2 | semidirect |
| 5. C29×#1827 | C2 | semidirect |
| 12. C29×#533 | C4 | semidirect |
| 14. C2×C29×#124 | C4 | semidirect |
| 15. C29×#519 | C4 | semidirect |
| 16. C29×#518 | C4 | semidirect |
| 124. #12723 | C29 | direct (N × H) |
| 160. #2123 | C2×C29 | semidirect |
| 161. #1827 | C2×C29 | semidirect |
| 186. #533 | C4×C29 | semidirect |
| 188. C2×#124 | C4×C29 | semidirect |
| 189. #519 | C4×C29 | semidirect |
| 190. #518 | C4×C29 | semidirect |
| 252. C29 | #12723 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3510 | 2 |
| C29×#2134 | 2 |
| C29×#2128 | 2 |
| C29×#2123 | 2 |
| C29×#1827 | 2 |
| #12723 | 29 |