Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
200 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 70 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 | #2206 |
| commutator, Frattini, cosocle | C2×C16 | C23×C29 |
| prime radical | C29×#2263 | C2 |
| LCS | G ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C2×C4×C29 ◁ C4×C8×C29 ◁ C4×C16×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#2264 | C2 | semidirect |
| 3. C29×#2249 | C2 | semidirect |
| 4. C29×#2178 | C2 | semidirect |
| 5. C29×#1422 | C2 | semidirect |
| 6. C29×#1420 | C2 | semidirect |
| 7. C29×#1419 | C2 | semidirect |
| 66. #13691 | C29 | direct (N × H) |
| 84. #2264 | C2×C29 | semidirect |
| 86. #2249 | C2×C29 | semidirect |
| 87. #2178 | C2×C29 | semidirect |
| 88. #1422 | C2×C29 | semidirect |
| 89. #1420 | C2×C29 | semidirect |
| 90. #1419 | C2×C29 | semidirect |
| 140. C29 | #13691 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2264 | 2 |
| C29×#2263 | 2 |
| C29×#2249 | 2 |
| C29×#2178 | 2 |
| C29×#1422 | 2 |
| C29×#1420 | 2 |
| C29×#1419 | 2 |
| #13691 | 29 |