Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 139 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. #19128052 | C2 | semidirect |
| 4. #19128037 | C2 | semidirect |
| 5. #19127997 | C2 | semidirect |
| 6. #19127942 | C2 | semidirect |
| 7. #19127912 | C2 | semidirect |
| 8. #19127859 | C2 | semidirect |
| 9. C4×Dic332 | C2 | semidirect |
| 10. C2×#14581717 | C2 | semidirect |
| 77. D4×C83 | Q16 | semidirect |
| 123. C83 | #3299 | semidirect |
| 208. D4 | Dic332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128408 | 2 |
| D4×Dic166 | 2 |
| #19128052 | 2 |
| #19128037 | 2 |
| #19127997 | 2 |
| #19127942 | 2 |
| #19127912 | 2 |
| #19127859 | 2 |
| C4×Dic332 | 2 |
| C2×#14581717 | 2 |
| C8×D4×C83 | 2 |
| #3299 | 83 |