Finite Group DatabasebetaFinite Group DatabasebetaOrder 29504.
266 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 140 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. #28414205 | C2 | direct (N × H) |
| 2. C2×#20301511 | C2 | semidirect |
| 3. C2×#20301510 | C2 | semidirect |
| 4. C2×D461⋊C8 | C2 | semidirect |
| 5. C22×#16814786 | C2 | semidirect |
| 7. #20301511 | C22 | semidirect |
| 8. #20301510 | C22 | semidirect |
| 9. D461⋊C8 | C22 | semidirect |
| 13. C2×#16814786 | C22 | semidirect |
| 46. C2×C461 | #131 | semidirect |
| 49. C461 | C2×#131 | semidirect |
| 97. C2 | #28414205 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28414205 | 2 |
| C2×#20301511 | 2 |
| C2×#20301510 | 2 |
| C2×D461⋊C8 | 2 |
| C22×#16814786 | 2 |
| C2×#20301500 | 2 |
| C2×#131 | 461 |