Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
584 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#14581818 | C2 | semidirect |
| 2. C4×#13050590 | C2 | semidirect |
| 3. #19127898 | C2 | semidirect |
| 4. #19127893 | C2 | semidirect |
| 5. #19127725 | C2 | semidirect |
| 6. #19127706 | C2 | semidirect |
| 7. C2×#127×C83 | C2 | semidirect |
| 10. C2×#13050578 | C22 | semidirect |
| 11. C2×#13050575 | C22 | semidirect |
| 13. C4×Dic166 | C22 | semidirect |
| 14. C4×D332 | C22 | semidirect |
| 19. C4⋊(C83⋊C8) | C22 | semidirect |
| 20. #14581713 | C22 | semidirect |
| 28. #13050590 | D4 | semidirect |
| 78. D332 | C2×D4 | semidirect |
| 82. Dic166 | C2×D4 | semidirect |
| 94. C4×C83 | AGL(1,ℤ/8) | semidirect |
| 105. C83 | #3038 | semidirect |
| 107. C2×#127 | D83 | semidirect |
| 201. C4 | #14581818 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581818 | 2 |
| C4×#13050590 | 2 |
| #19127898 | 2 |
| #19127893 | 2 |
| #19127725 | 2 |
| #19127706 | 2 |
| C2×#127×C83 | 2 |
| #3038 | 83 |