Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
386 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 2. #19128039 | C2 | semidirect |
| 3. #19128039 | C2 | semidirect |
| 4. #19128034 | C2 | semidirect |
| 5. #19128029 | C2 | semidirect |
| 6. #19127744 | C2 | semidirect |
| 7. #19127737 | C2 | semidirect |
| 8. #19127710 | C2 | semidirect |
| 9. C2×#14581716 | C2 | semidirect |
| 127. C83 | #3097 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128184 | 2 |
| #19128039 | 2 |
| #19128034 | 2 |
| #19128029 | 2 |
| #19127744 | 2 |
| #19127737 | 2 |
| #19127710 | 2 |
| C2×#14581716 | 2 |
| #19127668 | 2 |
| #536×C83 | 2 |
| #3097 | 83 |