Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
1746 conjugacy classes of subgroups.
The subgroup lattice has 398 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C29 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C29 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C29 ◁ C2×C4×Q8×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#3390 | C2 | direct (N × H) |
| 49. C2×Q16×C29 | Q8 | semidirect |
| 120. Q16×C29 | C2×Q8 | semidirect |
| 150. C2×#3390 | C29 | direct (N × H) |
| 181. #3390 | C2×C29 | direct (N × H) |
| 240. C2×C29 | #3390 | direct (N × H) |
| 247. C2×Q16 | Q8×C29 | semidirect |
| 301. C29 | C2×#3390 | direct (N × H) |
| 319. Q16 | C2×Q8×C29 | semidirect |
| 393. C2 | C29×#3390 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#557 | 2 |
| C29×#3390 | 2 |
| C2×C29×#501 | 2 |
| C2×C29×#499 | 2 |
| C2×C29×#479 | 2 |
| C2×C29×#477 | 2 |
| C2×C29×#446 | 2 |
| C2×C29×#441 | 2 |
| C2×C4×Q16×C29 | 2 |
| C2×#3390 | 29 |