Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
312 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 97 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. #19127725 | C2 | semidirect |
| 4. #19127461 | C2 | semidirect |
| 5. C4×C4⋊C4×C83 | C2 | semidirect |
| 8. C4×Dic166 | C4 | semidirect |
| 9. C4×Dic166 | C4 | semidirect |
| 10. C4×D332 | C4 | semidirect |
| 11. C4×D332 | C4 | semidirect |
| 81. D332 | C4⋊C4 | semidirect |
| 87. Dic166 | C4⋊C4 | semidirect |
| 101. C4×C83 | #104 | semidirect |
| 116. C83 | #1806 | semidirect |
| 120. C4×C4⋊C4 | D83 | semidirect |
| 220. C4 | #14581720 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#13050590 | 2 |
| #19127725 | 2 |
| C2×#14581720 | 2 |
| #19127461 | 2 |
| C4×C4⋊C4×C83 | 2 |
| #1806 | 83 |