Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
314 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 110 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C29 | #329 |
| commutator | C42 | C22×C4×C29 |
| Frattini, cosocle | #97 | C23×C29 |
| prime radical | C23×C29 | #100 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C22×C4×C29 ◁ C2×C29×#97 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C29×#1356 | C2 | direct (N × H) |
| 56. C2×#1356 | C29 | direct (N × H) |
| 76. #1356 | C2×C29 | direct (N × H) |
| 99. C2×C29 | #1356 | direct (N × H) |
| 121. C29 | C2×#1356 | direct (N × H) |
| 173. C2 | C29×#1356 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#491 | 2 |
| C2×C29×#347 | 2 |
| C29×#1356 | 2 |
| C2×#1356 | 29 |