Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
672 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 153 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. #19127627 | C2 | semidirect |
| 3. #19127612 | C2 | semidirect |
| 4. #19127591 | C2 | semidirect |
| 5. #19127562 | C2 | semidirect |
| 7. C4×C22⋊Dic83 | C2 | semidirect |
| 8. C2×C22⋊Q8×C83 | C2 | semidirect |
| 17. C2×C4×Dic83 | C22 | semidirect |
| 18. C83⋊#95 | 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 |
| 111. C83 | #2561 | semidirect |
| 112. C2×C22⋊Q8 | D83 | semidirect |
| 121. C22×Q8 | C2×D83 | semidirect |
| 125. C2×C4⋊C4 | C2×D83 | semidirect |
| 126. 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 |
| #19127627 | 2 |
| #19127612 | 2 |
| #19127591 | 2 |
| #19127562 | 2 |
| #19127556 | 2 |
| C4×C22⋊Dic83 | 2 |
| C2×C22⋊Q8×C83 | 2 |
| #2561 | 83 |