Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
566 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 158 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 | C2×#102 |
| commutator | C2×C8 | C22×C4×C29 |
| Frattini, cosocle | C22×C8 | C23×C29 |
| prime radical | C2×C29×#493 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C2×C42×C29 ◁ C2×C4×C8×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#2150 | C2 | semidirect |
| 3. C2×C29×#361 | C2 | semidirect |
| 4. C4×C29×#108 | C2 | semidirect |
| 35. C29×#108 | D4 | semidirect |
| 67. #13257 | C29 | direct (N × H) |
| 90. #2150 | C2×C29 | semidirect |
| 91. C2×#361 | C2×C29 | semidirect |
| 92. C4×#108 | C2×C29 | semidirect |
| 100. C4×C29 | #361 | semidirect |
| 138. #108 | D4×C29 | semidirect |
| 143. C29 | #13257 | direct (N × H) |
| 199. C4 | C29×#361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#493 | 2 |
| C29×#2150 | 2 |
| C2×C29×#361 | 2 |
| C4×C29×#108 | 2 |
| #13257 | 29 |