Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
368 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 90 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 | #99 |
| commutator | C22×C4 | C2×C8×C29 |
| Frattini, cosocle | C2×#95 | C22×C29 |
| prime radical | C24×C29 | C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C29 ◁ C24×C29 ◁ C2×C29×#95 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 29. C29×#95 | C8 | semidirect |
| 71. #7122 | C29 | direct (N × H) |
| 190. #95 | C8×C29 | semidirect |
| 191. C29 | #7122 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#1442 | 2 |
| C29×#1280 | 2 |
| #7122 | 29 |