Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
856 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 856 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 | #1790 |
| commutator | C2×D4 | C22×C4×C29 |
| Frattini, cosocle | C2×#41 | C23×C29 |
| prime radical | C29×#3549 | C2 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C2×C4×C29 ◁ C2×#41×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#2132 | C2 | semidirect |
| 3. C29×#2122 | C2 | semidirect |
| 4. C29×#1914 | C2 | semidirect |
| 5. C29×#1884 | C2 | semidirect |
| 6. C29×#568 | C22 | semidirect |
| 8. C29×H(3,𝔽4) | C4 | semidirect |
| 12. D42×C29 | C4 | semidirect |
| 19. C29×#413 | C22 | semidirect |
| 21. C29×#410 | C22 | semidirect |
| 136. #12769 | C29 | direct (N × H) |
| 181. #2132 | C2×C29 | semidirect |
| 182. #2122 | C2×C29 | semidirect |
| 183. #1914 | C2×C29 | semidirect |
| 184. #1884 | C2×C29 | semidirect |
| 206. #568 | C22×C29 | semidirect |
| 208. H(3,𝔽4) | C4×C29 | semidirect |
| 212. D42 | C4×C29 | semidirect |
| 219. #413 | C22×C29 | semidirect |
| 221. #410 | C22×C29 | semidirect |
| 282. C29 | #12769 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3549 | 2 |
| C29×#2132 | 2 |
| C29×#2122 | 2 |
| C29×#1914 | 2 |
| C29×#1884 | 2 |
| #12769 | 29 |