Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
286 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C29 | #1616 |
| commutator, Frattini, cosocle | C2×M16 | C23×C29 |
| prime radical | C29×#3259 | C2 |
| LCS | G ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C2×C4×C29 ◁ C2×M16×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#2238 | C2 | semidirect |
| 3. C29×#2103 | C2 | semidirect |
| 4. C29×#1341 | C2 | semidirect |
| 5. C29×#1328 | C2 | semidirect |
| 64. #12304 | C29 | direct (N × H) |
| 83. #2238 | C2×C29 | semidirect |
| 84. #2103 | C2×C29 | semidirect |
| 85. #1341 | C2×C29 | semidirect |
| 86. #1328 | C2×C29 | semidirect |
| 135. C29 | #12304 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3259 | 2 |
| C29×#2238 | 2 |
| C29×#2103 | 2 |
| C29×#1341 | 2 |
| C29×#1328 | 2 |
| #12304 | 29 |