Finite Group DatabasebetaFinite Group DatabasebetaOrder 29504.
228 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #28414116 | C2 | semidirect |
| 2. #28414108 | C2 | semidirect |
| 3. #28414108 | C2 | semidirect |
| 4. #28414096 | C2 | semidirect |
| 5. #28414096 | C2 | semidirect |
| 6. #28414095 | C2 | semidirect |
| 7. #28414095 | C2 | semidirect |
| 8. #28414094 | C2 | semidirect |
| 9. #28414083 | C2 | semidirect |
| 13. C2×#20301480 | C2 | semidirect |
| 14. C4⋊C4×D461 | C2 | semidirect |
| 15. C22⋊Q8×C461 | C2 | semidirect |
| 54. C22⋊D461 | Q8 | semidirect |
| 101. C461 | #554 | semidirect |
| 111. C22⋊Q8 | D461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28414116 | 2 |
| #28414108 | 2 |
| #28414096 | 2 |
| #28414095 | 2 |
| #28414094 | 2 |
| #28414083 | 2 |
| C4×C22⋊D461 | 2 |
| #28414078 | 2 |
| C2×#20301480 | 2 |
| C4⋊C4×D461 | 2 |
| C22⋊Q8×C461 | 2 |
| #554 | 461 |