Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
322 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 109 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. #19128010 | C2 | semidirect |
| 3. #19128007 | C2 | semidirect |
| 6. #19127910 | C2 | semidirect |
| 7. #19127909 | C2 | semidirect |
| 100. C83 | #3261 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128311 | 2 |
| #19128010 | 2 |
| #19128007 | 2 |
| #19127957 | 2 |
| #19127942 | 2 |
| #19127910 | 2 |
| #19127909 | 2 |
| #19127727 | 2 |
| #467×C83 | 2 |
| #3261 | 83 |