Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
504 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 106 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 | C22×C4 | C22×C4×C29 |
| Frattini, cosocle | C2×C4⋊C4 | C23×C29 |
| prime radical | C2×C29×#127 | C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C22×C4×C29 ◁ C2×C4×D4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#1465 | C2 | semidirect |
| 3. C29×#1324 | C2 | semidirect |
| 4. C29×#1318 | C2 | semidirect |
| 53. C2×D4×C29 | M16 | semidirect |
| 77. C42×C29 | M16 | semidirect |
| 78. #11533 | C29 | direct (N × H) |
| 118. #1465 | C2×C29 | semidirect |
| 119. #1324 | C2×C29 | semidirect |
| 120. #1318 | C2×C29 | semidirect |
| 187. C29 | #11533 | direct (N × H) |
| 200. C2×D4 | M16×C29 | semidirect |
| 224. C42 | M16×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2328 | 2 |
| C29×#1465 | 2 |
| C29×#1324 | 2 |
| C29×#1318 | 2 |
| #11533 | 29 |