Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
284 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 79 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. #19127737 | C2 | semidirect |
| 3. #19127717 | C2 | semidirect |
| 4. #19127675 | C2 | semidirect |
| 5. #19127674 | C2 | semidirect |
| 6. #19127659 | C2 | semidirect |
| 7. #421×C83 | C2 | semidirect |
| 13. C2×#13050580 | C4 | semidirect |
| 14. C2×#13050578 | C4 | semidirect |
| 15. C2×#13050577 | C4 | semidirect |
| 16. C2×#13050575 | C4 | semidirect |
| 133. C83 | #1976 | semidirect |
| 137. #421 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581812 | 2 |
| #19127737 | 2 |
| #19127717 | 2 |
| #19127675 | 2 |
| #19127674 | 2 |
| #19127659 | 2 |
| #421×C83 | 2 |
| #1976 | 83 |