Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
676 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 197 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×#14581792 | C2 | semidirect |
| 2. C2×#14581771 | C2 | semidirect |
| 3. #19127637 | C2 | semidirect |
| 5. #19127570 | C2 | semidirect |
| 6. C4×C4⋊Dic83 | C2 | semidirect |
| 30. C4⋊Dic83 | D4 | semidirect |
| 37. C2×D4×C83 | Q8 | semidirect |
| 82. C4×C83 | C22⋊Q8 | semidirect |
| 93. C83 | #2542 | semidirect |
| 122. C2×D4 | Dic166 | semidirect |
| 177. C4 | #14581771 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581792 | 2 |
| C2×#14581771 | 2 |
| #19127637 | 2 |
| #19127604 | 2 |
| #19127570 | 2 |
| C4×C4⋊Dic83 | 2 |
| C2×C4×D4×C83 | 2 |
| #2542 | 83 |