Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
346 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 346 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. #19128175 | C2 | semidirect |
| 3. #19127719 | C2 | semidirect |
| 4. #19127705 | C2 | semidirect |
| 5. #19127674 | C2 | semidirect |
| 6. #19127472 | C2 | semidirect |
| 7. H(3,ℤ/4)×C83 | C2 | semidirect |
| 12. C2×#13050579 | C4 | semidirect |
| 13. C2×D664 | C4 | semidirect |
| 30. C2×Dic166 | C2×C4 | semidirect |
| 35. C2×D332 | C2×C4 | semidirect |
| 53. C2×C8×C83 | C2×C4 | semidirect |
| 116. C83 | #1904 | semidirect |
| 123. H(3,ℤ/4) | D83 | semidirect |
| 165. C2×C8 | C4×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581820 | 2 |
| #19128175 | 2 |
| #19127719 | 2 |
| #19127705 | 2 |
| #19127674 | 2 |
| #19127472 | 2 |
| H(3,ℤ/4)×C83 | 2 |
| #1904 | 83 |