Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
362 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 122 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×#102 |
| commutator | C2×C8 | C22×C4×C29 |
| Frattini, cosocle | C4×C8 | C23×C29 |
| prime radical | C29×#3169 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C2×C42×C29 ◁ C2×C4×C8×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C29×#346 | C2 | semidirect |
| 3. C29×#1568 | C2 | semidirect |
| 4. C29×#1333 | C2 | semidirect |
| 74. #11678 | C29 | direct (N × H) |
| 101. C2×#346 | C2×C29 | semidirect |
| 102. #1568 | C2×C29 | semidirect |
| 103. #1333 | C2×C29 | semidirect |
| 165. C29 | #11678 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3169 | 2 |
| C2×C29×#346 | 2 |
| C29×#1568 | 2 |
| C29×#1333 | 2 |
| #11678 | 29 |