Finite Group DatabasebetaFinite Group DatabasebetaOrder 1984.
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. C31×H(5,𝔽2) | C2 | semidirect |
| 2. #11758566 | C2 | semidirect |
| 3. #11758527 | C2 | semidirect |
| 4. #11758526 | C2 | semidirect |
| 5. #11758525 | C2 | semidirect |
| 6. #11758509 | C2 | semidirect |
| 7. C2×#92479 | C2 | semidirect |
| 10. #41×C31 | C22 | semidirect |
| 12. C2×D4×C31 | C22 | semidirect |
| 15. #92495 | C22 | semidirect |
| 16. C2×D124 | C22 | semidirect |
| 17. #92482 | C22 | semidirect |
| 18. #92481 | C22 | semidirect |
| 19. #92480 | C22 | semidirect |
| 20. #92479 | C22 | semidirect |
| 21. #92479 | C22 | semidirect |
| 22. #92474 | C22 | semidirect |
| 23. C2×C31⋊C8 | C22 | semidirect |
| 56. H(5,𝔽2) | D31 | semidirect |
| 62. C31 | #576 | semidirect |
| 67. #41 | C2×D31 | semidirect |
| 71. C2×D4 | C2×D31 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C31×H(5,𝔽2) | 2 |
| #11758566 | 2 |
| #11758527 | 2 |
| #11758526 | 2 |
| #11758525 | 2 |
| #11758509 | 2 |
| C2×#92479 | 2 |
| #576 | 31 |