Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
3158 conjugacy classes of subgroups.
The subgroup lattice has 392 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C29 | C24 |
| commutator | C22 | C24×C4×C29 |
| Frattini, cosocle | C23 | C25×C29 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C29×#2365 | C2 | direct (N × H) |
| 11. C2×C29×C4⋊Q8 | C4 | semidirect |
| 48. C29×C4⋊Q8 | C2×C4 | semidirect |
| 56. C2×C4⋊C4×C29 | Q8 | semidirect |
| 119. C4⋊C4×C29 | C2×Q8 | semidirect |
| 124. C2×#2365 | C29 | direct (N × H) |
| 155. C2×C4×C29 | C4×Q8 | semidirect |
| 168. #2365 | C2×C29 | direct (N × H) |
| 196. C4×C29 | C2×C4×Q8 | semidirect |
| 198. C2×C4⋊Q8 | C4×C29 | semidirect |
| 223. C2×C29 | #2365 | direct (N × H) |
| 243. C4⋊Q8 | C2×C4×C29 | semidirect |
| 251. C2×C4⋊C4 | Q8×C29 | semidirect |
| 271. C29 | C2×#2365 | direct (N × H) |
| 315. C4⋊C4 | C2×Q8×C29 | semidirect |
| 350. C2×C4 | C4×Q8×C29 | semidirect |
| 382. C4 | C2×C4×Q8×C29 | semidirect |
| 383. C2 | C29×#2365 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C29×C4⋊Q8 | 2 |
| C22×C4×Q8×C29 | 2 |
| C29×#2365 | 2 |
| C2×C29×#391 | 2 |
| C2×C29×#389 | 2 |
| C2×C29×#387 | 2 |
| C2×C4×C4⋊C4×C29 | 2 |
| C2×#2365 | 29 |