Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
638 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 638 conjugacy classes of subgroups — too many to draw. Only its 206 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 | D42 |
| commutator, Frattini, cosocle | C42 | C24×C29 |
| prime radical | C29×#1712 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#3396 | C2 | semidirect |
| 3. C29×#1668 | C2 | semidirect |
| 4. C29×#1620 | C2 | semidirect |
| 5. C8×Q16×C29 | C2 | semidirect |
| 56. #20021 | C29 | direct (N × H) |
| 72. #3396 | C2×C29 | semidirect |
| 74. #1668 | C2×C29 | semidirect |
| 75. #1620 | C2×C29 | semidirect |
| 76. C8×Q16 | C2×C29 | semidirect |
| 119. C29 | #20021 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3396 | 2 |
| C29×#1712 | 2 |
| C29×#1668 | 2 |
| C29×#1620 | 2 |
| C8×Q16×C29 | 2 |
| #20021 | 29 |