Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
328 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 328 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 | #1613 |
| commutator, Frattini, cosocle | C2×M16 | C23×C29 |
| prime radical | C29×#3197 | 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×#2239 | C2 | semidirect |
| 3. C29×#2238 | C2 | semidirect |
| 4. C29×#2091 | C2 | semidirect |
| 5. C29×#1342 | C2 | semidirect |
| 6. C29×#1341 | C2 | semidirect |
| 7. C29×#1320 | C2 | semidirect |
| 101. #12300 | C29 | direct (N × H) |
| 133. #2239 | C2×C29 | semidirect |
| 134. #2238 | C2×C29 | semidirect |
| 135. #2091 | C2×C29 | semidirect |
| 136. #1342 | C2×C29 | semidirect |
| 137. #1341 | C2×C29 | semidirect |
| 138. #1320 | C2×C29 | semidirect |
| 214. C29 | #12300 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3197 | 2 |
| C29×#2239 | 2 |
| C29×#2238 | 2 |
| C29×#2091 | 2 |
| C29×#1342 | 2 |
| C29×#1341 | 2 |
| C29×#1320 | 2 |
| #12300 | 29 |