Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
398 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 398 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 | C2×C42 | C23×C29 |
| prime radical | C29×#532 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#2605 | C2 | semidirect |
| 5. C29×#1300 | C2 | semidirect |
| 6. C29×#1288 | C2 | semidirect |
| 7. C29×#1285 | C2 | semidirect |
| 30. C29×C4⋊Q8 | Q8 | semidirect |
| 31. C29×#127 | Q8 | semidirect |
| 109. #10378 | C29 | direct (N × H) |
| 155. #2605 | C2×C29 | semidirect |
| 159. #1300 | C2×C29 | semidirect |
| 160. #1288 | C2×C29 | semidirect |
| 161. #1285 | C2×C29 | semidirect |
| 211. C4⋊Q8 | Q8×C29 | semidirect |
| 212. #127 | Q8×C29 | semidirect |
| 248. C29 | #10378 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2605 | 2 |
| C29×#1980 | 2 |
| C29×#1514 | 2 |
| C29×#1505 | 2 |
| C29×#1300 | 2 |
| C29×#1288 | 2 |
| C29×#1285 | 2 |
| #10378 | 29 |