Finite Group DatabasebetaFinite Group DatabasebetaOrder 29504.
188 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 45 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 |
|---|---|---|
| 2. C2×#20301490 | C2 | semidirect |
| 3. C2×#20301489 | C2 | semidirect |
| 4. #28414098 | C2 | semidirect |
| 5. #28414038 | C2 | semidirect |
| 6. #28414030 | C2 | semidirect |
| 7. #102×C461 | C2 | semidirect |
| 9. C2×Dic922 | C22 | semidirect |
| 17. C2×#16814779 | C22 | semidirect |
| 21. C2×C8×C461 | C22 | semidirect |
| 22. C4⋊C4×C461 | C22 | semidirect |
| 54. C2×D461 | SD16 | semidirect |
| 66. C461 | #450 | semidirect |
| 73. #102 | D461 | semidirect |
| 86. C2×C8 | C2×D461 | semidirect |
| 88. C4⋊C4 | C2×D461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×D461 | 2 |
| C2×#20301490 | 2 |
| C2×#20301489 | 2 |
| #28414098 | 2 |
| #28414038 | 2 |
| #28414030 | 2 |
| #102×C461 | 2 |
| #450 | 461 |