Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
804 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 804 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C29 | #120 |
| commutator, Frattini, cosocle | C23×C4 | C23×C29 |
| prime radical | C24×C29 | C2×D4 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C29 ◁ C23×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 77. C22×C4×C29 | Q16 | semidirect |
| 93. #9967 | C29 | direct (N × H) |
| 213. C29 | #9967 | direct (N × H) |
| 242. C22×C4 | Q16×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#451 | 2 |
| C29×#2659 | 2 |
| C2×C29×#328 | 2 |
| C29×#1446 | 2 |
| C29×#1280 | 2 |
| #9967 | 29 |