Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
336 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 113 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. #19128044 | C2 | semidirect |
| 3. #19128038 | C2 | semidirect |
| 4. #19128005 | C2 | semidirect |
| 5. #19127960 | C2 | semidirect |
| 6. C4×Dic332 | C2 | semidirect |
| 8. #19127740 | C2 | semidirect |
| 9. #499×C83 | C2 | semidirect |
| 97. C83 | #3352 | semidirect |
| 99. #499 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128389 | 2 |
| #19128044 | 2 |
| #19128038 | 2 |
| #19128005 | 2 |
| #19127960 | 2 |
| C4×Dic332 | 2 |
| #19127780 | 2 |
| #19127740 | 2 |
| #499×C83 | 2 |
| #3352 | 83 |