Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14581823 | C2 | semidirect |
| 3. #19128080 | C2 | semidirect |
| 4. #19127957 | C2 | semidirect |
| 5. #19127911 | C2 | semidirect |
| 6. #19127903 | C2 | semidirect |
| 7. #19127861 | C2 | semidirect |
| 8. #19127857 | C2 | semidirect |
| 9. C4×#13050577 | C2 | semidirect |
| 10. #19127779 | C2 | semidirect |
| 11. D4×Q8×C83 | C2 | semidirect |
| 53. #13050577 | D4 | semidirect |
| 124. C4×C83 | #137 | semidirect |
| 135. C83 | #3276 | semidirect |
| 137. D4×Q8 | D83 | semidirect |
| 261. C4 | #14581823 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581823 | 2 |
| #19128356 | 2 |
| #19128080 | 2 |
| #19127957 | 2 |
| #19127911 | 2 |
| #19127903 | 2 |
| #19127861 | 2 |
| #19127857 | 2 |
| C4×#13050577 | 2 |
| #19127779 | 2 |
| D4×Q8×C83 | 2 |
| #3276 | 83 |