Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
292 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 106 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 | #95 |
| commutator | C2×C4 | C4×C8×C29 |
| Frattini, cosocle | C23×C8 | C22×C29 |
| socle | C22×C29 | #336 |
| prime radical | C24×C29 | M16 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C29 ◁ C23×C8×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. C22×C16×C29 | C4 | semidirect |
| 13. C29×C22⋊C16 | C4 | semidirect |
| 62. #7200 | C29 | direct (N × H) |
| 112. C22×C16 | C4×C29 | semidirect |
| 119. C22⋊C16 | C4×C29 | semidirect |
| 146. C29 | #7200 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2112 | 2 |
| C2×C29×C22⋊C16 | 2 |
| C29×#1752 | 2 |
| #7200 | 29 |