Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
344 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 86 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 | #2127 |
| commutator | C42 | C22×C4×C29 |
| Frattini, cosocle | #124 | C23×C29 |
| prime radical | C29×#3220 | C2 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C22×C29 ◁ C22×C4×C29 ◁ C29×#535 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#2134 | C2 | semidirect |
| 3. C29×#2127 | C2 | semidirect |
| 4. C29×#1414 | C2 | semidirect |
| 5. C29×#1406 | C2 | semidirect |
| 6. C29×#540 | C4 | semidirect |
| 9. C29×#493 | C4 | semidirect |
| 10. C29×#490 | C4 | semidirect |
| 16. C29×#433 | C4 | semidirect |
| 31. C29×#127 | C2×C4 | semidirect |
| 33. C29×#125 | C2×C4 | semidirect |
| 54. C29×#97 | C2×C4 | semidirect |
| 55. C4×C8×C29 | C2×C4 | semidirect |
| 95. #13605 | C29 | direct (N × H) |
| 132. #2134 | C2×C29 | semidirect |
| 133. #2127 | C2×C29 | semidirect |
| 134. #1414 | C2×C29 | semidirect |
| 135. #1406 | C2×C29 | semidirect |
| 157. #540 | C4×C29 | semidirect |
| 160. #493 | C4×C29 | semidirect |
| 161. #490 | C4×C29 | semidirect |
| 167. #433 | C4×C29 | semidirect |
| 189. #127 | C2×C4×C29 | semidirect |
| 191. #125 | C2×C4×C29 | semidirect |
| 212. #97 | C2×C4×C29 | semidirect |
| 213. C4×C8 | C2×C4×C29 | semidirect |
| 214. C29 | #13605 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3220 | 2 |
| C29×#2134 | 2 |
| C29×#2127 | 2 |
| C29×#1414 | 2 |
| C29×#1406 | 2 |
| #13605 | 29 |