Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
476 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 98 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×C22⋊C4 | C23×C29 |
| prime radical | C29×#2631 | C2 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ 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×#1799 | C2 | semidirect |
| 3. C29×#1465 | C2 | semidirect |
| 4. C29×#1351 | C2 | semidirect |
| 5. C29×#1343 | C2 | semidirect |
| 6. C2×C29×#124 | C4 | semidirect |
| 11. C29×#393 | C4 | semidirect |
| 14. C29×#392 | C4 | semidirect |
| 18. C29×#383 | C4 | semidirect |
| 107. #11825 | C29 | direct (N × H) |
| 164. #1799 | C2×C29 | semidirect |
| 165. #1465 | C2×C29 | semidirect |
| 166. #1351 | C2×C29 | semidirect |
| 167. #1343 | C2×C29 | semidirect |
| 202. C2×#124 | C4×C29 | semidirect |
| 207. #393 | C4×C29 | semidirect |
| 210. #392 | C4×C29 | semidirect |
| 214. #383 | C4×C29 | semidirect |
| 262. C29 | #11825 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2631 | 2 |
| C29×#1799 | 2 |
| C29×#1465 | 2 |
| C29×#1351 | 2 |
| C29×#1343 | 2 |
| #11825 | 29 |