Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 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. D4×Dic166 | C2 | semidirect |
| 2. #19128366 | C2 | semidirect |
| 3. #19128105 | C2 | semidirect |
| 4. #19128104 | C2 | semidirect |
| 5. #19127982 | C2 | semidirect |
| 6. #19127980 | C2 | semidirect |
| 7. #19127979 | C2 | semidirect |
| 8. #19127825 | C2 | semidirect |
| 11. #474×C83 | C2 | semidirect |
| 51. #13050575 | Q8 | semidirect |
| 78. D4×C83 | C2×Q8 | semidirect |
| 91. D332 | C2×Q8 | semidirect |
| 97. Dic166 | D8 | semidirect |
| 100. C83⋊C8 | C2×Q8 | semidirect |
| 124. C83 | Q8×D8 | semidirect |
| 132. #474 | D83 | semidirect |
| 208. D4 | Q8×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic166 | 2 |
| #19128366 | 2 |
| #19128105 | 2 |
| #19128104 | 2 |
| #19127982 | 2 |
| #19127980 | 2 |
| #19127979 | 2 |
| #19127825 | 2 |
| C4×#13050575 | 2 |
| #19127781 | 2 |
| #474×C83 | 2 |
| Q8×D8 | 83 |