Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
384 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14581783 | C2 | semidirect |
| 3. #19128011 | C2 | semidirect |
| 4. #19128007 | C2 | semidirect |
| 5. #19128004 | C2 | semidirect |
| 6. #19128000 | C2 | semidirect |
| 7. #19127744 | C2 | semidirect |
| 8. #19127724 | C2 | semidirect |
| 11. #428×C83 | C2 | semidirect |
| 136. C83 | #3080 | semidirect |
| 144. #428 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581783 | 2 |
| #19128169 | 2 |
| #19128011 | 2 |
| #19128007 | 2 |
| #19128004 | 2 |
| #19128000 | 2 |
| #19127744 | 2 |
| #19127724 | 2 |
| #19127703 | 2 |
| #19127700 | 2 |
| #428×C83 | 2 |
| #3080 | 83 |