Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
444 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 129 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. #19128034 | C2 | semidirect |
| 3. #19127978 | C2 | semidirect |
| 4. #19127903 | C2 | semidirect |
| 6. #19127799 | C2 | semidirect |
| 7. #19127758 | C2 | semidirect |
| 8. #533×C83 | C2 | semidirect |
| 18. #14581725 | C22 | semidirect |
| 19. C4⋊(C83⋊C8) | C22 | semidirect |
| 20. #14581716 | C22 | semidirect |
| 23. #14581703 | C22 | semidirect |
| 24. C4⋊Q8×C83 | C22 | semidirect |
| 25. C4⋊Q8×C83 | C22 | semidirect |
| 30. C4×Q8×C83 | C22 | semidirect |
| 113. C83 | #3110 | semidirect |
| 114. #533 | D83 | semidirect |
| 125. C4⋊Q8 | C2×D83 | semidirect |
| 126. C4⋊Q8 | C2×D83 | semidirect |
| 131. C4×Q8 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D332 | 2 |
| #19128034 | 2 |
| #19127978 | 2 |
| #19127903 | 2 |
| #19127851 | 2 |
| #19127799 | 2 |
| #19127758 | 2 |
| #533×C83 | 2 |
| #3110 | 83 |