Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
528 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 122 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 | #127 |
| commutator, Frattini, cosocle | C2×C42 | C23×C29 |
| socle | C22×C29 | #392 |
| prime radical | C23×C29 | #120 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C29 ◁ C2×C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 75. C42×C29 | Q16 | semidirect |
| 79. #10017 | C29 | direct (N × H) |
| 166. C29 | #10017 | direct (N × H) |
| 193. C42 | Q16×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3104 | 2 |
| C29×#2399 | 2 |
| C29×#1995 | 2 |
| C29×#1487 | 2 |
| C29×#1274 | 2 |
| #10017 | 29 |