Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
698 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 106 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 | #392 |
| commutator, Frattini, cosocle | C23×C4 | C23×C29 |
| prime radical | C29×#3192 | C2 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#2504 | C2 | semidirect |
| 3. C29×#2501 | C2 | semidirect |
| 4. C29×#1821 | C2 | semidirect |
| 5. C29×#1507 | C2 | semidirect |
| 6. C29×#1507 | C2 | semidirect |
| 7. C29×#1297 | C2 | semidirect |
| 130. #10328 | C29 | direct (N × H) |
| 180. #2504 | C2×C29 | semidirect |
| 181. #2501 | C2×C29 | semidirect |
| 182. #1821 | C2×C29 | semidirect |
| 183. #1507 | C2×C29 | semidirect |
| 184. #1507 | C2×C29 | semidirect |
| 185. #1297 | C2×C29 | semidirect |
| 290. C29 | #10328 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3192 | 2 |
| C29×#2504 | 2 |
| C29×#2501 | 2 |
| C29×#1821 | 2 |
| C29×#1507 | 2 |
| C29×#1297 | 2 |
| #10328 | 29 |