Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
360 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 107 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. M16×Dic83 | C2 | semidirect |
| 4. #19127470 | C2 | semidirect |
| 5. #343×C83 | C2 | semidirect |
| 13. #14581708 | C4 | semidirect |
| 29. #13050574 | C2×C4 | semidirect |
| 37. M16×C83 | C2×C4 | semidirect |
| 78. Dic83 | #100 | semidirect |
| 86. C83 | C4×#100 | semidirect |
| 91. #343 | D83 | semidirect |
| 119. M16 | C4×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581754 | 2 |
| C2×#14581708 | 2 |
| M16×Dic83 | 2 |
| #19127470 | 2 |
| #343×C83 | 2 |
| C4×#100 | 83 |