Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
578 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 134 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 | C22×C4 | C22×C4×C29 |
| Frattini, cosocle | C2×C42 | C23×C29 |
| prime radical | C29×#2619 | C2 |
| LCS | G ▷ C22×C4 ▷ 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 |
|---|---|---|
| 1. C29×#2921 | C2 | semidirect |
| 3. C29×#1545 | C2 | semidirect |
| 4. C29×#1458 | C2 | semidirect |
| 5. C29×#1286 | C2 | semidirect |
| 46. C29×C4⋊C8 | D4 | semidirect |
| 94. #9198 | C29 | direct (N × H) |
| 135. #2921 | C2×C29 | semidirect |
| 137. #1545 | C2×C29 | semidirect |
| 138. #1458 | C2×C29 | semidirect |
| 139. #1286 | C2×C29 | semidirect |
| 212. C4⋊C8 | D4×C29 | semidirect |
| 220. C29 | #9198 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2921 | 2 |
| C29×#2619 | 2 |
| C29×#1545 | 2 |
| C29×#1458 | 2 |
| C29×#1286 | 2 |
| #9198 | 29 |