Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
620 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 118 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 | #386 |
| commutator | C42 | C22×C4×C29 |
| Frattini, cosocle | C2×C42 | C23×C29 |
| prime radical | C29×#3151 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#2380 | C2 | semidirect |
| 3. C29×#1555 | C2 | semidirect |
| 4. C29×#1514 | C2 | semidirect |
| 5. C29×#1288 | C2 | semidirect |
| 10. C29×#493 | C4 | semidirect |
| 11. C29×#492 | C4 | semidirect |
| 28. C29×C4⋊Q8 | C2×C4 | semidirect |
| 31. C29×#127 | C2×C4 | semidirect |
| 43. C4×C8×C29 | C2×C4 | semidirect |
| 80. #9428 | C29 | direct (N × H) |
| 111. #2380 | C2×C29 | semidirect |
| 112. #1555 | C2×C29 | semidirect |
| 113. #1514 | C2×C29 | semidirect |
| 114. #1288 | C2×C29 | semidirect |
| 135. #493 | C4×C29 | semidirect |
| 136. #492 | C4×C29 | semidirect |
| 158. C4⋊Q8 | C2×C4×C29 | semidirect |
| 161. #127 | C2×C4×C29 | semidirect |
| 173. C4×C8 | C2×C4×C29 | semidirect |
| 177. C29 | #9428 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3151 | 2 |
| C29×#2380 | 2 |
| C29×#1555 | 2 |
| C29×#1514 | 2 |
| C29×#1288 | 2 |
| #9428 | 29 |