Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
356 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 2. #19128105 | C2 | semidirect |
| 3. #19128102 | C2 | semidirect |
| 4. #19128101 | C2 | semidirect |
| 5. #19128098 | C2 | semidirect |
| 31. C2×C83⋊C8 | Q8 | semidirect |
| 44. C2×C8×C83 | Q8 | semidirect |
| 79. C83 | #3160 | semidirect |
| 114. C2×C8 | Dic166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128254 | 2 |
| #19128105 | 2 |
| #19128102 | 2 |
| #19128101 | 2 |
| #19128098 | 2 |
| #19127739 | 2 |
| #19127737 | 2 |
| C2×C8×Dic83 | 2 |
| #427×C83 | 2 |
| #3160 | 83 |