Finite Group DatabasebetaFinite Group DatabasebetaOrder 29504.
268 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 107 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. #28414164 | C2 | semidirect |
| 2. #28414144 | C2 | semidirect |
| 3. #28414143 | C2 | semidirect |
| 4. #28414138 | C2 | semidirect |
| 5. C2×#20301486 | C2 | semidirect |
| 6. #28414125 | C2 | semidirect |
| 7. H(5,𝔽2)×C461 | C2 | semidirect |
| 9. #20301501 | C22 | semidirect |
| 10. C2×D1844 | C22 | semidirect |
| 12. #20301491 | C22 | semidirect |
| 13. #20301489 | C22 | semidirect |
| 14. #20301488 | C22 | semidirect |
| 15. #20301486 | C22 | semidirect |
| 16. #20301486 | C22 | semidirect |
| 17. #20301485 | C22 | semidirect |
| 18. C2×#16814779 | C22 | semidirect |
| 21. #41×C461 | C22 | semidirect |
| 23. C2×D4×C461 | C22 | semidirect |
| 54. C461 | #576 | semidirect |
| 57. H(5,𝔽2) | D461 | semidirect |
| 67. #41 | C2×D461 | semidirect |
| 71. C2×D4 | C2×D461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28414164 | 2 |
| #28414144 | 2 |
| #28414143 | 2 |
| #28414138 | 2 |
| C2×#20301486 | 2 |
| #28414125 | 2 |
| H(5,𝔽2)×C461 | 2 |
| #576 | 461 |