Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
544 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 197 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. C2×#14581757 | C2 | semidirect |
| 4. #19127798 | C2 | direct (N × H) |
| 5. C2×#14581725 | C2 | semidirect |
| 6. C2×#14581717 | C2 | semidirect |
| 7. C2×#14581702 | C2 | semidirect |
| 11. C2×#13050578 | C4 | semidirect |
| 15. #14581757 | C22 | semidirect |
| 23. #14581725 | C22 | semidirect |
| 24. #14581717 | C22 | semidirect |
| 25. #14581702 | C22 | semidirect |
| 32. C2×Dic166 | C2×C4 | semidirect |
| 40. #13050578 | C2×C4 | semidirect |
| 41. C2×C83⋊C8 | C2×C4 | semidirect |
| 86. Dic166 | C22×C4 | semidirect |
| 88. C83⋊C8 | C22×C4 | semidirect |
| 106. C2×C83 | #440 | semidirect |
| 111. C83 | C2×#440 | semidirect |
| 217. C2 | #19127798 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13050578 | 2 |
| C2×#14581757 | 2 |
| C2×D4×Dic83 | 2 |
| #19127798 | 2 |
| C2×#14581725 | 2 |
| C2×#14581717 | 2 |
| C2×#14581702 | 2 |
| C2×#102×C83 | 2 |
| C2×#440 | 83 |