Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
346 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 89 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. #19127719 | C2 | semidirect |
| 3. #19127706 | C2 | semidirect |
| 4. #19127674 | C2 | semidirect |
| 5. #19127471 | C2 | semidirect |
| 6. #19127457 | C2 | semidirect |
| 7. #518×C83 | C2 | semidirect |
| 11. C2×#13050578 | C4 | semidirect |
| 12. C2×#13050575 | C4 | semidirect |
| 29. C2×Dic166 | C2×C4 | semidirect |
| 30. C2×D332 | C2×C4 | semidirect |
| 40. C2×C83⋊C8 | C2×C4 | semidirect |
| 116. C83 | #1904 | semidirect |
| 118. #518 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581818 | 2 |
| #19127719 | 2 |
| #19127706 | 2 |
| #19127674 | 2 |
| #19127471 | 2 |
| #19127457 | 2 |
| #518×C83 | 2 |
| #1904 | 83 |