Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
|---|---|---|
| 1. C2×#14581792 | C2 | semidirect |
| 3. #19127997 | C2 | semidirect |
| 4. #19127992 | C2 | semidirect |
| 5. #19127987 | C2 | semidirect |
| 6. #19127982 | C2 | semidirect |
| 7. #19127743 | C2 | semidirect |
| 9. #423×C83 | C2 | semidirect |
| 36. #13050590 | Q8 | semidirect |
| 89. D332 | C2×Q8 | semidirect |
| 96. Dic166 | C2×Q8 | semidirect |
| 122. C83 | #3079 | semidirect |
| 130. #423 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581792 | 2 |
| C4×#13050590 | 2 |
| #19127997 | 2 |
| #19127992 | 2 |
| #19127987 | 2 |
| #19127982 | 2 |
| #19127743 | 2 |
| #19127703 | 2 |
| #423×C83 | 2 |
| #3079 | 83 |