Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
676 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×#14581781 | C2 | semidirect |
| 3. C2×Q8×Dic83 | C2 | semidirect |
| 4. #19127617 | C2 | semidirect |
| 5. #19127604 | C2 | semidirect |
| 6. #19127603 | C2 | semidirect |
| 7. #19127601 | C2 | semidirect |
| 8. C4×Dic83⋊C4 | C2 | semidirect |
| 9. C2×#124×C83 | C2 | semidirect |
| 55. C2×Q8×C83 | D4 | semidirect |
| 119. Dic83 | #124 | semidirect |
| 128. C83 | #2548 | semidirect |
| 131. C2×#124 | D83 | semidirect |
| 163. C2×Q8 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581788 | 2 |
| C2×#14581781 | 2 |
| C2×Q8×Dic83 | 2 |
| #19127617 | 2 |
| #19127604 | 2 |
| #19127603 | 2 |
| #19127601 | 2 |
| C4×Dic83⋊C4 | 2 |
| C2×#124×C83 | 2 |
| #2548 | 83 |