Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
512 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 2. #19127596 | C2 | semidirect |
| 3. #19127595 | C2 | semidirect |
| 4. #19127589 | C2 | semidirect |
| 5. #19127585 | C2 | semidirect |
| 7. #19127573 | C2 | semidirect |
| 8. #19127559 | C2 | semidirect |
| 12. #14581773 | C4 | semidirect |
| 36. C22×Dic83 | C2×C4 | semidirect |
| 44. Dic83⋊C4 | C2×C4 | semidirect |
| 48. C22⋊Dic83 | C2×C4 | semidirect |
| 127. C83 | #2376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581773 | 2 |
| #19127596 | 2 |
| #19127595 | 2 |
| #19127589 | 2 |
| #19127585 | 2 |
| #19127581 | 2 |
| #19127573 | 2 |
| #19127559 | 2 |
| #390×C83 | 2 |
| #2376 | 83 |