Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
446 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 90 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 | #393 |
| commutator, Frattini, cosocle | C23×C4 | C23×C29 |
| prime radical | C2×C29×#121 | C22 |
| 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 |
|---|---|---|
| 1. C29×#2665 | C2 | semidirect |
| 5. C29×#1305 | C2 | semidirect |
| 6. C29×#1297 | C2 | semidirect |
| 7. C29×#1284 | C2 | semidirect |
| 29. C22×D4×C29 | Q8 | semidirect |
| 41. C2×C4⋊C4×C29 | Q8 | semidirect |
| 116. #10382 | C29 | direct (N × H) |
| 172. #2665 | C2×C29 | semidirect |
| 176. #1305 | C2×C29 | semidirect |
| 177. #1297 | C2×C29 | semidirect |
| 178. #1284 | C2×C29 | semidirect |
| 238. C22×D4 | Q8×C29 | semidirect |
| 250. C2×C4⋊C4 | Q8×C29 | semidirect |
| 276. C29 | #10382 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2665 | 2 |
| C29×#1964 | 2 |
| C29×#1510 | 2 |
| C29×#1507 | 2 |
| C29×#1305 | 2 |
| C29×#1297 | 2 |
| C29×#1284 | 2 |
| #10382 | 29 |