Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
582 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 122 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 | #386 |
| commutator | C22×C4 | C22×C4×C29 |
| Frattini, cosocle | C23×C4 | C23×C29 |
| prime radical | C29×#2635 | C2 |
| LCS | G ▷ C22×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×#2973 | C2 | semidirect |
| 3. C4×C29×#99 | C2 | semidirect |
| 4. C29×#1507 | C2 | semidirect |
| 5. C29×#1284 | C2 | semidirect |
| 13. C29×#400 | C4 | semidirect |
| 14. C29×#399 | C4 | semidirect |
| 16. C29×#394 | C4 | semidirect |
| 18. C29×#392 | C4 | semidirect |
| 55. C29×C22⋊C8 | D4 | semidirect |
| 112. #9185 | C29 | direct (N × H) |
| 164. #2973 | C2×C29 | semidirect |
| 166. C4×#99 | C2×C29 | semidirect |
| 167. #1507 | C2×C29 | semidirect |
| 168. #1284 | C2×C29 | semidirect |
| 208. #400 | C4×C29 | semidirect |
| 209. #399 | C4×C29 | semidirect |
| 211. #394 | C4×C29 | semidirect |
| 213. #392 | C4×C29 | semidirect |
| 258. C22⋊C8 | D4×C29 | semidirect |
| 266. C29 | #9185 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2973 | 2 |
| C29×#2635 | 2 |
| C4×C29×#99 | 2 |
| C29×#1507 | 2 |
| C29×#1284 | 2 |
| #9185 | 29 |