Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
344 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 82 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 | #447 |
| commutator, Frattini, cosocle | C4×C8 | C23×C29 |
| prime radical | C29×#3277 | C2 |
| LCS | G ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C42×C29 ◁ C29×#436 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#2243 | C2 | semidirect |
| 3. C29×#2225 | C2 | semidirect |
| 4. C29×#1695 | C2 | semidirect |
| 5. C29×#1360 | C2 | semidirect |
| 6. C29×#1334 | C2 | semidirect |
| 7. C29×#1330 | C2 | semidirect |
| 106. #12377 | C29 | direct (N × H) |
| 138. #2243 | C2×C29 | semidirect |
| 139. #2225 | C2×C29 | semidirect |
| 140. #1695 | C2×C29 | semidirect |
| 141. #1360 | C2×C29 | semidirect |
| 142. #1334 | C2×C29 | semidirect |
| 143. #1330 | C2×C29 | semidirect |
| 219. C29 | #12377 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3277 | 2 |
| C29×#2243 | 2 |
| C29×#2225 | 2 |
| C29×#1695 | 2 |
| C29×#1360 | 2 |
| C29×#1334 | 2 |
| C29×#1330 | 2 |
| #12377 | 29 |