Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 1. C22×Dic332 | C2 | semidirect |
| 2. C2×Q16×D83 | C2 | semidirect |
| 4. #19128079 | C2 | semidirect |
| 5. #19127943 | C2 | semidirect |
| 6. #19127910 | C2 | semidirect |
| 7. #19127858 | C2 | semidirect |
| 8. #19127856 | C2 | semidirect |
| 9. #19127795 | C2 | semidirect |
| 11. #467×C83 | C2 | semidirect |
| 55. Dic332 | D4 | semidirect |
| 90. C22⋊D83 | Q16 | semidirect |
| 112. C22×C83 | C2×Q16 | semidirect |
| 116. C2×D83 | C2×Q16 | semidirect |
| 126. Dic83 | C2×Q16 | semidirect |
| 133. C83 | D4×Q16 | semidirect |
| 139. #467 | D83 | semidirect |
| 248. C22 | Q16×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic332 | 2 |
| C2×Q16×D83 | 2 |
| #19128364 | 2 |
| #19128079 | 2 |
| #19127943 | 2 |
| #19127910 | 2 |
| #19127858 | 2 |
| #19127856 | 2 |
| #19127795 | 2 |
| C8×C22⋊D83 | 2 |
| #467×C83 | 2 |
| D4×Q16 | 83 |