Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
306 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 67 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×#14581719 | C2 | semidirect |
| 3. C2×#14581718 | C2 | semidirect |
| 4. #19127700 | C2 | semidirect |
| 5. #19127570 | C2 | semidirect |
| 6. #19127469 | C2 | semidirect |
| 7. #417×C83 | C2 | semidirect |
| 48. C4×Dic83 | D4 | semidirect |
| 129. C83 | #2039 | semidirect |
| 134. #417 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128279 | 2 |
| C2×#14581719 | 2 |
| C2×#14581718 | 2 |
| #19127700 | 2 |
| #19127570 | 2 |
| #19127469 | 2 |
| #417×C83 | 2 |
| #2039 | 83 |