Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
360 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C29 | #1555 |
| commutator | C42 | C22×C4×C29 |
| Frattini, cosocle | C4×C8 | C23×C29 |
| prime radical | C29×#532 | C4 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C2×C4×C29 ◁ C4×M16×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#2165 | C2 | semidirect |
| 3. C29×#1359 | C2 | semidirect |
| 4. C29×#1358 | C2 | semidirect |
| 69. #11993 | C29 | direct (N × H) |
| 93. #2165 | C2×C29 | semidirect |
| 94. #1359 | C2×C29 | semidirect |
| 95. #1358 | C2×C29 | semidirect |
| 147. C29 | #11993 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3152 | 2 |
| C29×#2165 | 2 |
| C29×#1359 | 2 |
| C29×#1358 | 2 |
| #11993 | 29 |