Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
182 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C29 | #327 |
| commutator | C2×C8 | C2×C8×C29 |
| Frattini, cosocle | C2×#97 | C22×C29 |
| socle | C2×C29 | #1271 |
| prime radical | C23×C29 | #104 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C29 ◁ C22×C4×C29 ◁ C2×C29×#97 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 21. C29×#106 | C8 | semidirect |
| 49. #7125 | C29 | direct (N × H) |
| 102. #106 | C8×C29 | semidirect |
| 109. C29 | #7125 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#1946 | 2 |
| C29×#1375 | 2 |
| C29×#1281 | 2 |
| #7125 | 29 |