Finite Group DatabasebetaFinite Group DatabasebetaOrder 29504.
212 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 97 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. #28414117 | C2 | semidirect |
| 2. #28414113 | C2 | semidirect |
| 3. #28414111 | C2 | semidirect |
| 5. #28414094 | C2 | semidirect |
| 6. Q8×Dic461 | C2 | semidirect |
| 7. #28414083 | C2 | semidirect |
| 9. #28414077 | C2 | semidirect |
| 10. #28414076 | C2 | semidirect |
| 11. C22⋊Q8×C461 | C2 | semidirect |
| 72. C461 | #556 | semidirect |
| 79. C22⋊Q8 | D461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28414117 | 2 |
| #28414113 | 2 |
| #28414111 | 2 |
| #28414104 | 2 |
| #28414094 | 2 |
| Q8×Dic461 | 2 |
| #28414083 | 2 |
| C4×C22⋊D461 | 2 |
| #28414077 | 2 |
| #28414076 | 2 |
| C22⋊Q8×C461 | 2 |
| #556 | 461 |