Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
568 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 568 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 | 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 |
|---|---|---|
| 2. C29×#3095 | C2 | semidirect |
| 4. C29×#1996 | C2 | semidirect |
| 5. C29×#1826 | C2 | semidirect |
| 7. C29×#1305 | C2 | semidirect |
| 138. #9936 | C29 | direct (N × H) |
| 188. #3095 | C2×C29 | semidirect |
| 190. #1996 | C2×C29 | semidirect |
| 191. #1826 | C2×C29 | semidirect |
| 193. #1305 | C2×C29 | semidirect |
| 305. C29 | #9936 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3193 | 2 |
| C29×#3095 | 2 |
| C29×#2624 | 2 |
| C29×#1996 | 2 |
| C29×#1826 | 2 |
| C29×#1507 | 2 |
| C29×#1305 | 2 |
| #9936 | 29 |