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. #19128366 | C2 | semidirect |
| 2. #19128105 | C2 | semidirect |
| 3. #19127980 | C2 | semidirect |
| 4. #19127978 | C2 | semidirect |
| 5. C8×Dic166 | C2 | semidirect |
| 8. #500×C83 | C2 | semidirect |
| 34. D664 | Q8 | semidirect |
| 59. D332 | C2×Q8 | semidirect |
| 63. Dic166 | D8 | semidirect |
| 65. C8×C83 | C2×Q8 | semidirect |
| 84. C83 | Q8×D8 | semidirect |
| 87. #500 | D83 | semidirect |
| 150. C8 | Q8×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128366 | 2 |
| #19128105 | 2 |
| #19127980 | 2 |
| #19127978 | 2 |
| C8×Dic166 | 2 |
| C4×D664 | 2 |
| #19127783 | 2 |
| #500×C83 | 2 |
| Q8×D8 | 83 |