Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
544 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 544 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 | #392 |
| commutator, Frattini, cosocle | C23×C4 | C23×C29 |
| prime radical | C29×#3186 | C2 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#3094 | C2 | semidirect |
| 3. C29×#1818 | C2 | semidirect |
| 4. C29×#1471 | C2 | semidirect |
| 5. C29×#1293 | C2 | semidirect |
| 82. #9977 | C29 | direct (N × H) |
| 113. #3094 | C2×C29 | semidirect |
| 114. #1818 | C2×C29 | semidirect |
| 115. #1471 | C2×C29 | semidirect |
| 116. #1293 | C2×C29 | semidirect |
| 185. C29 | #9977 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3186 | 2 |
| C29×#3094 | 2 |
| C29×#1818 | 2 |
| C29×#1471 | 2 |
| C29×#1293 | 2 |
| #9977 | 29 |