Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
880 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 126 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 | C24 | C22×C4×C29 |
| Frattini, cosocle | C23×C4 | C23×C29 |
| prime radical | C29×#2408 | C2 |
| LCS | G ▷ C24 ▷ 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 |
|---|---|---|
| 1. C29×#2973 | C2 | semidirect |
| 3. C29×#1783 | C2 | semidirect |
| 4. C29×#1465 | C2 | semidirect |
| 5. C29×#1305 | C2 | semidirect |
| 34. C2×M16×C29 | D4 | semidirect |
| 108. #9503 | C29 | direct (N × H) |
| 130. C23×C29 | #100 | semidirect |
| 159. #2973 | C2×C29 | semidirect |
| 161. #1783 | C2×C29 | semidirect |
| 162. #1465 | C2×C29 | semidirect |
| 163. #1305 | C2×C29 | semidirect |
| 231. C2×M16 | D4×C29 | semidirect |
| 255. C29 | #9503 | direct (N × H) |
| 327. C23 | C29×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2973 | 2 |
| C29×#2408 | 2 |
| C29×#1783 | 2 |
| C29×#1465 | 2 |
| C29×#1305 | 2 |
| #9503 | 29 |