Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
248 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 78 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 | #459 |
| commutator, Frattini, cosocle | C4×C8 | C23×C29 |
| prime radical | C29×#2206 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C42×C29 ◁ C82×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C29×#2226 | C2 | semidirect |
| 3. C29×#1706 | C2 | semidirect |
| 4. C29×#1589 | C2 | semidirect |
| 5. C29×#1370 | C2 | semidirect |
| 6. C29×#1365 | C2 | semidirect |
| 7. C29×#1361 | C2 | semidirect |
| 71. #12485 | C29 | direct (N × H) |
| 96. #2226 | C2×C29 | semidirect |
| 98. #1706 | C2×C29 | semidirect |
| 99. #1589 | C2×C29 | semidirect |
| 100. #1370 | C2×C29 | semidirect |
| 101. #1365 | C2×C29 | semidirect |
| 102. #1361 | C2×C29 | semidirect |
| 159. C29 | #12485 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2226 | 2 |
| C29×#2206 | 2 |
| C29×#1706 | 2 |
| C29×#1589 | 2 |
| C29×#1370 | 2 |
| C29×#1365 | 2 |
| C29×#1361 | 2 |
| #12485 | 29 |