Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
362 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 362 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 |
|---|---|---|
| 3. #19128011 | C2 | semidirect |
| 4. #19128007 | C2 | semidirect |
| 5. #19127995 | C2 | semidirect |
| 6. #19127985 | C2 | semidirect |
| 44. C2×Dic166 | Q8 | semidirect |
| 117. C83 | #3082 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128329 | 2 |
| #19128178 | 2 |
| #19128011 | 2 |
| #19128007 | 2 |
| #19127995 | 2 |
| #19127985 | 2 |
| #19127744 | 2 |
| #19127727 | 2 |
| #19127709 | 2 |
| C2×#14581717 | 2 |
| #427×C83 | 2 |
| #3082 | 83 |