Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
634 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 634 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 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C29 |
| LCS | G ▷ C2×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 |
|---|---|---|
| 1. C29×#3245 | C2 | semidirect |
| 2. C29×#3036 | C2 | semidirect |
| 3. C29×#1954 | C2 | semidirect |
| 4. C29×#1492 | C2 | semidirect |
| 5. C29×#1292 | C2 | semidirect |
| 66. C2×D4×C29 | D8 | semidirect |
| 95. #10254 | C29 | direct (N × H) |
| 135. #3245 | C2×C29 | semidirect |
| 136. #3036 | C2×C29 | semidirect |
| 137. #1954 | C2×C29 | semidirect |
| 138. #1492 | C2×C29 | semidirect |
| 139. #1292 | C2×C29 | semidirect |
| 215. C29 | #10254 | direct (N × H) |
| 229. C2×D4 | D8×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3245 | 2 |
| C29×#3036 | 2 |
| C29×#1954 | 2 |
| C29×#1492 | 2 |
| C29×#1292 | 2 |
| #10254 | 29 |