Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
294 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 158 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C29 | C2×C42 |
| commutator | C2×C4 | C2×C42×C29 |
| Frattini, cosocle | C2×C42 | C23×C29 |
| socle | C22×C29 | #376 |
| prime radical | C23×C29 | #117 |
| LCS | G ▷ C2×C4 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 12. C29×#322 | C4 | semidirect |
| 13. C29×#322 | C4 | semidirect |
| 14. C82×C29 | C4 | semidirect |
| 44. #8142 | C29 | direct (N × H) |
| 78. #322 | C4×C29 | semidirect |
| 79. #322 | C4×C29 | semidirect |
| 80. C82 | C4×C29 | semidirect |
| 99. C29 | #8142 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#1746 | 2 |
| C29×#1452 | 2 |
| C29×#1450 | 2 |
| C29×#1275 | 2 |
| C29×#1274 | 2 |
| #8142 | 29 |