Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
366 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 98 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 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C29 |
| prime radical | C29×#532 | C22 |
| 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 |
|---|---|---|
| 2. C29×#1997 | C2 | semidirect |
| 3. C29×#1574 | C2 | semidirect |
| 5. C29×#1546 | C2 | semidirect |
| 7. C29×#1299 | C2 | semidirect |
| 100. #10491 | C29 | direct (N × H) |
| 135. #1997 | C2×C29 | semidirect |
| 136. #1574 | C2×C29 | semidirect |
| 138. #1546 | C2×C29 | semidirect |
| 140. #1299 | C2×C29 | semidirect |
| 218. C29 | #10491 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3227 | 2 |
| C29×#1997 | 2 |
| C29×#1574 | 2 |
| C29×#1560 | 2 |
| C29×#1546 | 2 |
| C29×#1484 | 2 |
| C29×#1299 | 2 |
| #10491 | 29 |