Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
306 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 142 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 | #117 |
| commutator | C2×C4 | C22×C8×C29 |
| Frattini, cosocle | C2×C42 | C23×C29 |
| socle | C22×C29 | #383 |
| prime radical | C23×C29 | #117 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C29 ◁ C2×C29×#97 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 29. C4×C8×C29 | C8 | semidirect |
| 54. #8800 | C29 | direct (N × H) |
| 116. C4×C8 | C8×C29 | semidirect |
| 117. C29 | #8800 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C29×#97 | 2 |
| C29×#1281 | 2 |
| C29×#1276 | 2 |
| C29×#1275 | 2 |
| #8800 | 29 |