Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
578 conjugacy classes of subgroups; only the 214 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 214 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 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C29 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C2×C42×C29 ◁ C2×C4×C8×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#3169 | C2 | semidirect |
| 2. C29×#2224 | C2 | semidirect |
| 3. C29×#2215 | C2 | semidirect |
| 4. C29×#2206 | C2 | semidirect |
| 5. C2×C29×C4⋊C16 | C2 | semidirect |
| 68. #33811 | C29 | direct (N × H) |
| 82. C2×C4×C29 | D16 | semidirect |
| 91. #3169 | C2×C29 | semidirect |
| 92. #2224 | C2×C29 | semidirect |
| 93. #2215 | C2×C29 | semidirect |
| 94. #2206 | C2×C29 | semidirect |
| 95. C2×C4⋊C16 | C2×C29 | semidirect |
| 150. C29 | #33811 | direct (N × H) |
| 190. C2×C4 | C29×D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3169 | 2 |
| C29×#2224 | 2 |
| C29×#2215 | 2 |
| C29×#2206 | 2 |
| C2×C29×C4⋊C16 | 2 |
| #33811 | 29 |