Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
286 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 97 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. #19127743 | C2 | semidirect |
| 4. #19127567 | C2 | semidirect |
| 5. #19127469 | C2 | semidirect |
| 6. #19127461 | C2 | semidirect |
| 25. #104×C83 | C4 | semidirect |
| 54. M16×C83 | C2×C4 | semidirect |
| 57. C42×C83 | C2×C4 | semidirect |
| 112. C83 | #1860 | semidirect |
| 134. #104 | Dic83 | semidirect |
| 154. M16 | C2×Dic83 | semidirect |
| 169. C42 | C2×Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128184 | 2 |
| #19127743 | 2 |
| #19127702 | 2 |
| #19127567 | 2 |
| #19127469 | 2 |
| #19127461 | 2 |
| C2×#104×C83 | 2 |
| #1860 | 83 |