Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
1334 conjugacy classes of subgroups; only the 290 normal subgroups are shown.
This group has 1334 conjugacy classes of subgroups — too many to draw. Only its 290 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 | #2847 |
| commutator, Frattini, cosocle | C22×C4 | C24×C29 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C22×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#3573 | C2 | semidirect |
| 2. C29×#3058 | C2 | semidirect |
| 3. C29×#3027 | C2 | semidirect |
| 4. C29×#1910 | C2 | semidirect |
| 5. C29×#1812 | C2 | semidirect |
| 7. C22×D8×C29 | C22 | semidirect |
| 16. C29×#427 | C22 | semidirect |
| 17. C29×#418 | C22 | semidirect |
| 19. C29×H(3,ℤ/4) | C22 | semidirect |
| 35. C2×M16×C29 | D4 | semidirect |
| 38. C22×C8×C29 | D4 | semidirect |
| 82. #32948 | C29 | direct (N × H) |
| 106. #3573 | C2×C29 | semidirect |
| 107. #3058 | C2×C29 | semidirect |
| 108. #3027 | C2×C29 | semidirect |
| 109. #1910 | C2×C29 | semidirect |
| 110. #1812 | C2×C29 | semidirect |
| 123. C22×D8 | C22×C29 | semidirect |
| 132. #427 | C22×C29 | semidirect |
| 133. #418 | C22×C29 | semidirect |
| 135. H(3,ℤ/4) | C22×C29 | semidirect |
| 155. C2×M16 | D4×C29 | semidirect |
| 158. C22×C8 | D4×C29 | semidirect |
| 169. C29 | #32948 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3573 | 2 |
| C29×#3058 | 2 |
| C29×#3027 | 2 |
| C29×#1910 | 2 |
| C29×#1812 | 2 |
| #32948 | 29 |