Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
500 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 126 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×#99 |
| commutator | C22×C4 | C22×C4×C29 |
| Frattini, cosocle | C22×D4 | C23×C29 |
| prime radical | C22×D4×C29 | C23 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C22×C4×C29 ◁ C2×C4×D4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C2×C29×C4⋊Q8 | C4 | semidirect |
| 12. C29×#382 | C4 | semidirect |
| 16. C4×C4⋊C4×C29 | C4 | semidirect |
| 44. C29×#99 | Q8 | semidirect |
| 91. #13299 | C29 | direct (N × H) |
| 166. C2×C4⋊Q8 | C4×C29 | semidirect |
| 173. #382 | C4×C29 | semidirect |
| 177. C4×C4⋊C4 | C4×C29 | semidirect |
| 213. #99 | Q8×C29 | semidirect |
| 219. C29 | #13299 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2563 | 2 |
| C29×#1799 | 2 |
| C4×C29×#99 | 2 |
| C29×#1393 | 2 |
| #13299 | 29 |