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. C2×Q16×D83 | C2 | semidirect |
| 3. #19127939 | C2 | semidirect |
| 4. #19127908 | C2 | semidirect |
| 5. #19127855 | C2 | semidirect |
| 6. C4×Dic332 | C2 | semidirect |
| 8. #494×C83 | C2 | semidirect |
| 36. Dic332 | D4 | semidirect |
| 65. D332 | Q16 | semidirect |
| 78. C2×D83 | C2×Q16 | semidirect |
| 81. C4×C83 | C2×Q16 | semidirect |
| 92. C83 | D4×Q16 | semidirect |
| 95. #494 | D83 | semidirect |
| 176. C4 | Q16×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D83 | 2 |
| #19128366 | 2 |
| #19127939 | 2 |
| #19127908 | 2 |
| #19127855 | 2 |
| C4×Dic332 | 2 |
| C8×D332 | 2 |
| #494×C83 | 2 |
| D4×Q16 | 83 |