Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
1184 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 1184 conjugacy classes of subgroups — too many to draw. Only its 130 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 | C24 | C22×C4×C29 |
| Frattini, cosocle | C25 | C23×C29 |
| prime radical | C29×#2403 | C2 |
| LCS | G ▷ C24 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C25×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#2309 | C2 | semidirect |
| 3. C29×#1781 | C2 | semidirect |
| 4. C29×#1781 | C2 | semidirect |
| 5. C29×#1304 | C2 | semidirect |
| 9. C2×C29×#120 | C4 | semidirect |
| 16. C29×#386 | C4 | semidirect |
| 53. C2×C22⋊C4×C29 | D4 | semidirect |
| 125. #9497 | C29 | direct (N × H) |
| 194. C2×C4×C29 | #99 | semidirect |
| 196. #2309 | C2×C29 | semidirect |
| 197. #1781 | C2×C29 | semidirect |
| 198. #1781 | C2×C29 | semidirect |
| 199. #1304 | C2×C29 | semidirect |
| 243. C2×#120 | C4×C29 | semidirect |
| 250. #386 | C4×C29 | semidirect |
| 297. C2×C22⋊C4 | D4×C29 | semidirect |
| 302. C29 | #9497 | direct (N × H) |
| 438. C2×C4 | C29×#99 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2403 | 2 |
| C29×#2309 | 2 |
| C29×#1781 | 2 |
| C29×#1304 | 2 |
| #9497 | 29 |