Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
244 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 82 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 | #466 |
| commutator, Frattini, cosocle | C4×C8 | C23×C29 |
| prime radical | C29×#2246 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C42×C29 ◁ C8×Q8×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#2183 | C2 | semidirect |
| 3. C29×#1668 | C2 | semidirect |
| 4. C29×#1372 | C2 | semidirect |
| 5. C29×#1361 | C2 | semidirect |
| 51. C16×C29 | SD16 | semidirect |
| 52. #12442 | C29 | direct (N × H) |
| 71. #2183 | C2×C29 | semidirect |
| 72. #1668 | C2×C29 | semidirect |
| 73. #1372 | C2×C29 | semidirect |
| 74. #1361 | C2×C29 | semidirect |
| 116. C29 | #12442 | direct (N × H) |
| 135. C16 | SD16×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2246 | 2 |
| C29×#2183 | 2 |
| C29×#1668 | 2 |
| C29×#1372 | 2 |
| C29×#1361 | 2 |
| #12442 | 29 |