Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 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. #19128005 | C2 | semidirect |
| 3. #19127998 | C2 | semidirect |
| 4. #19127988 | C2 | semidirect |
| 5. #19127983 | C2 | semidirect |
| 6. #19127744 | C2 | semidirect |
| 7. C2×#14581723 | C2 | semidirect |
| 8. #19127728 | C2 | semidirect |
| 11. #544×C83 | C2 | semidirect |
| 42. #13050590 | Q8 | semidirect |
| 124. C83 | #3084 | semidirect |
| 125. #544 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128181 | 2 |
| #19128005 | 2 |
| #19127998 | 2 |
| #19127988 | 2 |
| #19127983 | 2 |
| #19127744 | 2 |
| C2×#14581723 | 2 |
| #19127728 | 2 |
| #19127700 | 2 |
| #19127695 | 2 |
| #544×C83 | 2 |
| #3084 | 83 |