Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
558 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 122 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 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C29 |
| prime radical | C29×#3150 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C22×C4×C29 ◁ C2×C29×#97 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C29×#510 | C2 | semidirect |
| 3. C2×C29×#360 | C2 | semidirect |
| 4. C29×#1971 | C2 | semidirect |
| 5. C29×#1377 | C2 | semidirect |
| 35. C2×Q16×C29 | D4 | semidirect |
| 52. C29×M32 | D4 | semidirect |
| 102. #13342 | C29 | direct (N × H) |
| 135. C2×#510 | C2×C29 | semidirect |
| 137. C2×#360 | C2×C29 | semidirect |
| 138. #1971 | C2×C29 | semidirect |
| 139. #1377 | C2×C29 | semidirect |
| 188. C2×Q16 | D4×C29 | semidirect |
| 205. M32 | D4×C29 | semidirect |
| 211. C29 | #13342 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#510 | 2 |
| C29×#3150 | 2 |
| C2×C29×#360 | 2 |
| C29×#1971 | 2 |
| C29×#1377 | 2 |
| #13342 | 29 |