Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
466 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 114 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 | #381 |
| commutator | C22×C4 | C22×C4×C29 |
| Frattini, cosocle | C23×C4 | C23×C29 |
| prime radical | C22×D4×C29 | D4 |
| LCS | G ▷ C22×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 |
|---|---|---|
| 4. C29×#1297 | C2 | semidirect |
| 5. C29×#1284 | C2 | semidirect |
| 12. C29×#382 | C4 | semidirect |
| 13. C29×#381 | C4 | semidirect |
| 16. C4×C4⋊C4×C29 | C4 | semidirect |
| 17. C4×C22⋊C4×C29 | C4 | semidirect |
| 95. #8779 | C29 | direct (N × H) |
| 143. #1297 | C2×C29 | semidirect |
| 144. #1284 | C2×C29 | semidirect |
| 177. #382 | C4×C29 | semidirect |
| 178. #381 | C4×C29 | semidirect |
| 181. C4×C4⋊C4 | C4×C29 | semidirect |
| 182. C4×C22⋊C4 | C4×C29 | semidirect |
| 227. C29 | #8779 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2357 | 2 |
| C4×C29×#99 | 2 |
| C29×#1465 | 2 |
| C29×#1297 | 2 |
| C29×#1284 | 2 |
| #8779 | 29 |