Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
404 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 141 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. D4×Dic166 | C2 | semidirect |
| 2. #19128106 | C2 | semidirect |
| 3. #19128105 | C2 | semidirect |
| 4. #19127981 | C2 | semidirect |
| 5. #19127979 | C2 | semidirect |
| 6. C8×Dic166 | C2 | semidirect |
| 43. D8×C83 | Q8 | semidirect |
| 51. D4×C83 | C2×Q8 | semidirect |
| 63. Dic166 | D8 | direct (N × H) |
| 65. C8×C83 | C2×Q8 | semidirect |
| 84. C83 | Q8×D8 | semidirect |
| 119. D8 | Dic166 | direct (N × H) |
| 138. D4 | C2×Dic166 | semidirect |
| 150. C8 | C2×Dic166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic166 | 2 |
| #19128106 | 2 |
| #19128105 | 2 |
| #19127981 | 2 |
| #19127979 | 2 |
| C8×Dic166 | 2 |
| D8×Dic83 | 2 |
| C4×D8×C83 | 2 |
| Q8×D8 | 83 |