Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
346 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 346 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 | #1598 |
| commutator, Frattini, cosocle | C2×M16 | C23×C29 |
| prime radical | C29×#2190 | C2 |
| LCS | G ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C2×C4×C29 ◁ C2×M16×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#3256 | C2 | semidirect |
| 2. C29×#2191 | C2 | semidirect |
| 4. C29×#2050 | C2 | semidirect |
| 5. C29×#1342 | C2 | semidirect |
| 6. C29×#1341 | C2 | semidirect |
| 7. C29×#1327 | C2 | semidirect |
| 116. #12175 | C29 | direct (N × H) |
| 149. #3256 | C2×C29 | semidirect |
| 150. #2191 | C2×C29 | semidirect |
| 152. #2050 | C2×C29 | semidirect |
| 153. #1342 | C2×C29 | semidirect |
| 154. #1341 | C2×C29 | semidirect |
| 155. #1327 | C2×C29 | semidirect |
| 238. C29 | #12175 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3256 | 2 |
| C29×#2191 | 2 |
| C29×#2190 | 2 |
| C29×#2050 | 2 |
| C29×#1342 | 2 |
| C29×#1341 | 2 |
| C29×#1327 | 2 |
| #12175 | 29 |