Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
598 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 598 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 |
| 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×#3341 | C2 | semidirect |
| 2. C29×#1713 | C2 | semidirect |
| 3. C29×#1675 | C2 | semidirect |
| 4. C29×#1634 | C2 | semidirect |
| 5. C8×D8×C29 | C2 | semidirect |
| 54. #20019 | C29 | direct (N × H) |
| 70. #3341 | C2×C29 | semidirect |
| 71. #1713 | C2×C29 | semidirect |
| 72. #1675 | C2×C29 | semidirect |
| 73. #1634 | C2×C29 | semidirect |
| 74. C8×D8 | C2×C29 | semidirect |
| 118. C29 | #20019 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3341 | 2 |
| C29×#1713 | 2 |
| C29×#1675 | 2 |
| C29×#1634 | 2 |
| C8×D8×C29 | 2 |
| #20019 | 29 |