Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
778 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 106 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×#2404 | C2 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C24×C29 ◁ C22×C22⋊C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C29×#342 | C2 | semidirect |
| 3. C29×#1462 | C2 | semidirect |
| 4. C29×#1351 | C2 | semidirect |
| 5. C29×#1343 | C2 | semidirect |
| 6. C22×#41×C29 | C4 | semidirect |
| 11. C29×#393 | C4 | semidirect |
| 13. C29×#392 | C4 | semidirect |
| 18. C29×#381 | C4 | semidirect |
| 27. C22×Q8×C29 | C2×C4 | semidirect |
| 31. C22×D4×C29 | C2×C4 | semidirect |
| 58. C29×#95 | C2×C4 | semidirect |
| 59. C29×#95 | C2×C4 | semidirect |
| 124. #11753 | C29 | direct (N × H) |
| 198. C2×#342 | C2×C29 | semidirect |
| 199. #1462 | C2×C29 | semidirect |
| 200. #1351 | C2×C29 | semidirect |
| 201. #1343 | C2×C29 | semidirect |
| 246. C22×#41 | C4×C29 | semidirect |
| 251. #393 | C4×C29 | semidirect |
| 253. #392 | C4×C29 | semidirect |
| 258. #381 | C4×C29 | semidirect |
| 278. C22×Q8 | C2×C4×C29 | semidirect |
| 282. C22×D4 | C2×C4×C29 | semidirect |
| 309. #95 | C2×C4×C29 | semidirect |
| 310. #95 | C2×C4×C29 | semidirect |
| 311. C29 | #11753 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2404 | 2 |
| C2×C29×#342 | 2 |
| C29×#1462 | 2 |
| C29×#1351 | 2 |
| C29×#1343 | 2 |
| #11753 | 29 |