Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 117 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. C4×#13050574 | C2 | semidirect |
| 4. #19127469 | C2 | semidirect |
| 5. C4×M16×C83 | C2 | semidirect |
| 15. #14581708 | C4 | direct (N × H) |
| 32. #13050574 | C2×C4 | semidirect |
| 42. M16×C83 | C2×C4 | semidirect |
| 85. C4×C83 | #100 | semidirect |
| 96. C83 | C4×#100 | semidirect |
| 100. C4×M16 | D83 | semidirect |
| 133. M16 | C4×D83 | semidirect |
| 182. C4 | #14581708 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D332 | 2 |
| C2×#14581708 | 2 |
| C4×#13050574 | 2 |
| #19127469 | 2 |
| C4×M16×C83 | 2 |
| C4×#100 | 83 |