Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
330 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 102 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 | #397 |
| commutator, Frattini, cosocle | C2×C42 | C23×C29 |
| prime radical | C22×D4×C29 | D4 |
| 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 |
|---|---|---|
| 3. C29×#1570 | C2 | semidirect |
| 5. C29×#1301 | C2 | semidirect |
| 6. C29×#1286 | C2 | semidirect |
| 7. C29×#1286 | C2 | semidirect |
| 86. #10642 | C29 | direct (N × H) |
| 123. #1570 | C2×C29 | semidirect |
| 125. #1301 | C2×C29 | semidirect |
| 126. #1286 | C2×C29 | semidirect |
| 127. #1286 | C2×C29 | semidirect |
| 196. C29 | #10642 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#1804 | 2 |
| C29×#1800 | 2 |
| C29×#1570 | 2 |
| C29×#1478 | 2 |
| C29×#1301 | 2 |
| C29×#1286 | 2 |
| #10642 | 29 |