Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
520 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 230 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C29 | C2×#95 |
| commutator | C23 | C2×C42×C29 |
| Frattini, cosocle | C2×C42 | C23×C29 |
| prime radical | C24×C29 | C42 |
| LCS | G ▷ C23 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C22×C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#1309 | C2 | semidirect |
| 32. #8130 | C29 | direct (N × H) |
| 45. #1309 | C2×C29 | semidirect |
| 72. C29 | #8130 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2920 | 2 |
| C29×#1309 | 2 |
| #8130 | 29 |