Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
490 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 90 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 | C2×AΣL(1,𝔽16) |
| commutator | C2×D4 | C22×C4×C29 |
| Frattini, cosocle | #127 | C23×C29 |
| prime radical | C29×#3018 | C2 |
| LCS | G ▷ C2×D4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C2×C4×C29 ◁ C22×C4×C29 ◁ C29×#532 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#2126 | C2 | semidirect |
| 3. C29×#1560 | C2 | semidirect |
| 4. C29×#1402 | C2 | semidirect |
| 5. C29×#585 | C4 | semidirect |
| 9. C29×#455 | C4 | semidirect |
| 14. C29×#413 | C4 | semidirect |
| 17. C29×#353 | C22 | semidirect |
| 19. C29×#331 | C22 | semidirect |
| 107. #13562 | C29 | direct (N × H) |
| 153. #2126 | C2×C29 | semidirect |
| 154. #1560 | C2×C29 | semidirect |
| 155. #1402 | C2×C29 | semidirect |
| 176. #585 | C4×C29 | semidirect |
| 180. #455 | C4×C29 | semidirect |
| 185. #413 | C4×C29 | semidirect |
| 188. #353 | C22×C29 | semidirect |
| 190. #331 | C22×C29 | semidirect |
| 230. C29 | #13562 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3018 | 2 |
| C29×#2126 | 2 |
| C29×#1560 | 2 |
| C29×#1402 | 2 |
| #13562 | 29 |