Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
654 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 102 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 | C2×C42 | C23×C29 |
| prime radical | C29×#2540 | C2 |
| 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×#3215 | C2 | semidirect |
| 2. C29×#3110 | C2 | semidirect |
| 4. C29×#1986 | C2 | semidirect |
| 5. C29×#1527 | C2 | semidirect |
| 6. C29×#1490 | C2 | semidirect |
| 7. C29×#1285 | C2 | semidirect |
| 42. C29×C4⋊Q8 | D4 | semidirect |
| 43. C29×C4⋊Q8 | D4 | semidirect |
| 72. C29×C4⋊C8 | D4 | semidirect |
| 81. C29×#97 | D4 | semidirect |
| 143. #10008 | C29 | direct (N × H) |
| 193. #3215 | C2×C29 | semidirect |
| 194. #3110 | C2×C29 | semidirect |
| 196. #1986 | C2×C29 | semidirect |
| 197. #1527 | C2×C29 | semidirect |
| 198. #1490 | C2×C29 | semidirect |
| 199. #1285 | C2×C29 | semidirect |
| 269. C4⋊Q8 | D4×C29 | semidirect |
| 270. C4⋊Q8 | D4×C29 | semidirect |
| 299. C4⋊C8 | D4×C29 | semidirect |
| 308. #97 | D4×C29 | semidirect |
| 311. C29 | #10008 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3215 | 2 |
| C29×#3110 | 2 |
| C29×#2540 | 2 |
| C29×#1986 | 2 |
| C29×#1527 | 2 |
| C29×#1490 | 2 |
| C29×#1285 | 2 |
| #10008 | 29 |