Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
384 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 170 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C29 | C22⋊C4 |
| commutator | C2×C4 | C2×C42×C29 |
| Frattini, cosocle | C2×C42 | C23×C29 |
| socle | C22×C29 | C4×C22⋊C4 |
| prime radical | C23×C29 | #117 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C29 ◁ C2×C4×C8×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 61. #8242 | C29 | direct (N × H) |
| 129. C29 | #8242 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2960 | 2 |
| C29×#1544 | 2 |
| C29×#1526 | 2 |
| C8×M16×C29 | 2 |
| C29×#1299 | 2 |
| #8242 | 29 |