Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
714 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 110 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×#99 |
| commutator | C24 | C22×C4×C29 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C29 |
| prime radical | C23×D4×C29 | C4 |
| LCS | G ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C24×C29 ◁ C22×C22⋊C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#1462 | C2 | semidirect |
| 3. C29×#1317 | C2 | semidirect |
| 4. C29×#1316 | C2 | semidirect |
| 58. C24×C29 | M16 | semidirect |
| 83. C22×C4×C29 | M16 | semidirect |
| 95. #11502 | C29 | direct (N × H) |
| 152. #1462 | C2×C29 | semidirect |
| 153. #1317 | C2×C29 | semidirect |
| 154. #1316 | C2×C29 | semidirect |
| 241. C29 | #11502 | direct (N × H) |
| 255. C24 | M16×C29 | semidirect |
| 280. C22×C4 | M16×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2308 | 2 |
| C29×#1462 | 2 |
| C29×#1317 | 2 |
| C29×#1316 | 2 |
| #11502 | 29 |