Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
412 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 412 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 | C2×#102 |
| commutator | C2×C8 | C22×C4×C29 |
| Frattini, cosocle | C22×C8 | C23×C29 |
| prime radical | C24×C29 | D8 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C23×C4×C29 ◁ C23×C8×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C29×#1348 | C2 | semidirect |
| 5. C22×Q16×C29 | C4 | semidirect |
| 11. C29×#467 | C4 | semidirect |
| 13. C2×C29×#107 | C4 | semidirect |
| 87. #11889 | C29 | direct (N × H) |
| 124. #1348 | C2×C29 | semidirect |
| 144. C22×Q16 | C4×C29 | semidirect |
| 150. #467 | C4×C29 | semidirect |
| 152. C2×#107 | C4×C29 | semidirect |
| 194. C29 | #11889 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#467 | 2 |
| C29×#2112 | 2 |
| C29×#1807 | 2 |
| C29×#1348 | 2 |
| #11889 | 29 |