Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
390 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 129 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×C4×Dic166 | C2 | semidirect |
| 3. #19128032 | C2 | semidirect |
| 5. #19128009 | C2 | semidirect |
| 6. #19127924 | C2 | semidirect |
| 7. #19127859 | C2 | semidirect |
| 9. C4×Dic332 | C2 | semidirect |
| 10. C4×#13050579 | C2 | semidirect |
| 11. #431×C83 | C2 | semidirect |
| 132. C83 | #3108 | semidirect |
| 143. #431 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128235 | 2 |
| C2×C4×Dic166 | 2 |
| #19128032 | 2 |
| #19128015 | 2 |
| #19128009 | 2 |
| #19127924 | 2 |
| #19127859 | 2 |
| #19127842 | 2 |
| C4×Dic332 | 2 |
| C4×#13050579 | 2 |
| #431×C83 | 2 |
| #3108 | 83 |