Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
982 conjugacy classes of subgroups; only the 230 normal subgroups are shown.
This group has 982 conjugacy classes of subgroups — too many to draw. Only its 230 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×#120 |
| commutator, Frattini, cosocle | C42 | C24×C29 |
| prime radical | C2×C29×#555 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#3139 | C2 | semidirect |
| 3. C29×#3110 | C2 | semidirect |
| 4. C29×#1646 | C2 | semidirect |
| 5. C29×#1558 | C2 | semidirect |
| 6. C29×#1490 | C2 | semidirect |
| 17. C29×#487 | C22 | semidirect |
| 19. C29×#474 | C22 | semidirect |
| 20. C29×#461 | C22 | semidirect |
| 26. C29×#333 | C22 | semidirect |
| 27. C29×D4⋊C8 | C22 | semidirect |
| 104. #18552 | C29 | direct (N × H) |
| 133. #3139 | C2×C29 | semidirect |
| 134. #3110 | C2×C29 | semidirect |
| 135. #1646 | C2×C29 | semidirect |
| 136. #1558 | C2×C29 | semidirect |
| 137. #1490 | C2×C29 | semidirect |
| 162. #487 | C22×C29 | semidirect |
| 164. #474 | C22×C29 | semidirect |
| 165. #461 | C22×C29 | semidirect |
| 171. #333 | C22×C29 | semidirect |
| 172. D4⋊C8 | C22×C29 | semidirect |
| 216. C29 | #18552 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#555 | 2 |
| C29×#3139 | 2 |
| C29×#3110 | 2 |
| C29×#1646 | 2 |
| C29×#1558 | 2 |
| C29×#1490 | 2 |
| #18552 | 29 |