Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
470 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 146 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C29 | #1893 |
| commutator | C2×C8 | C22×C4×C29 |
| Frattini, cosocle | C22×C8 | C23×C29 |
| prime radical | C29×#3060 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C22×C4×C29 ◁ C2×C29×#131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#3407 | C2 | semidirect |
| 3. C29×#2145 | C2 | semidirect |
| 4. C29×#1812 | C2 | semidirect |
| 5. C29×#1386 | C2 | semidirect |
| 12. C29×#470 | C4 | semidirect |
| 13. C29×#469 | C4 | semidirect |
| 43. C29×M32 | D4 | semidirect |
| 90. #13077 | C29 | direct (N × H) |
| 119. #3407 | C2×C29 | semidirect |
| 121. #2145 | C2×C29 | semidirect |
| 122. #1812 | C2×C29 | semidirect |
| 123. #1386 | C2×C29 | semidirect |
| 145. #470 | C4×C29 | semidirect |
| 146. #469 | C4×C29 | semidirect |
| 181. M32 | D4×C29 | semidirect |
| 191. C29 | #13077 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3407 | 2 |
| C29×#3060 | 2 |
| C29×#2145 | 2 |
| C29×#1812 | 2 |
| C29×#1386 | 2 |
| #13077 | 29 |