Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
668 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 157 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. #19127636 | C2 | semidirect |
| 3. #19127623 | C2 | semidirect |
| 4. #19127612 | C2 | semidirect |
| 5. #19127573 | C2 | semidirect |
| 6. #19127561 | C2 | semidirect |
| 8. C2×C22⋊Q8×C83 | C2 | semidirect |
| 11. C2×C4⋊Dic83 | C22 | semidirect |
| 12. C2×Dic83⋊C4 | C22 | semidirect |
| 19. C83⋊#95 | C22 | semidirect |
| 20. C83⋊#95 | C22 | semidirect |
| 21. C22×Q8×C83 | C22 | semidirect |
| 24. C2×C4⋊C4×C83 | C22 | semidirect |
| 25. C2×C4⋊C4×C83 | C22 | semidirect |
| 31. C23×D83 | Q8 | semidirect |
| 118. C83 | #2626 | semidirect |
| 119. C2×C22⋊Q8 | D83 | semidirect |
| 128. C22×Q8 | C2×D83 | semidirect |
| 134. C2×C4⋊C4 | C2×D83 | semidirect |
| 135. C2×C4⋊C4 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×(C2×D83)⋊C4 | 2 |
| #19127636 | 2 |
| #19127623 | 2 |
| #19127612 | 2 |
| #19127573 | 2 |
| #19127561 | 2 |
| #19127556 | 2 |
| C2×C22⋊Q8×C83 | 2 |
| #2626 | 83 |