Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
200 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 74 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 | C2×D16 |
| commutator, Frattini, cosocle | C2×C16 | C23×C29 |
| prime radical | C29×#2215 | C2 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C22×C4×C29 ◁ C22×C8×C29 ◁ C22×C16×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C29×SD64 | C2 | semidirect |
| 2. C2×C29×M64 | C2 | semidirect |
| 3. C29×#2216 | C2 | semidirect |
| 5. C29×#1423 | C2 | semidirect |
| 6. C29×#1416 | C2 | semidirect |
| 7. C29×#1415 | C2 | semidirect |
| 39. C29×C32 | D4 | semidirect |
| 60. #13699 | C29 | direct (N × H) |
| 78. C2×SD64 | C2×C29 | semidirect |
| 79. C2×M64 | C2×C29 | semidirect |
| 80. #2216 | C2×C29 | semidirect |
| 82. #1423 | C2×C29 | semidirect |
| 83. #1416 | C2×C29 | semidirect |
| 84. #1415 | C2×C29 | semidirect |
| 134. C32 | D4×C29 | semidirect |
| 135. C29 | #13699 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×SD64 | 2 |
| C2×C29×M64 | 2 |
| C29×#2216 | 2 |
| C29×#2215 | 2 |
| C29×#1423 | 2 |
| C29×#1416 | 2 |
| C29×#1415 | 2 |
| #13699 | 29 |