Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
726 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C29 | #386 |
| commutator | C22×C4 | C22×C4×C29 |
| Frattini, cosocle | C23×C4 | C23×C29 |
| prime radical | C2×C29×#121 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#2310 | C2 | semidirect |
| 3. C29×#1784 | C2 | semidirect |
| 5. C29×#1284 | C2 | semidirect |
| 7. C2×C29×#124 | C4 | semidirect |
| 14. C29×#391 | C4 | semidirect |
| 97. #9466 | C29 | direct (N × H) |
| 140. #2310 | C2×C29 | semidirect |
| 141. #1784 | C2×C29 | semidirect |
| 143. #1284 | C2×C29 | semidirect |
| 167. C2×#124 | C4×C29 | semidirect |
| 174. #391 | C4×C29 | semidirect |
| 221. C29 | #9466 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2436 | 2 |
| C29×#2310 | 2 |
| C29×#1784 | 2 |
| C29×#1510 | 2 |
| C29×#1284 | 2 |
| #9466 | 29 |