Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
484 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 149 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×#14581814 | C2 | semidirect |
| 2. #19128279 | C2 | semidirect |
| 3. #19127947 | C2 | semidirect |
| 4. #19127942 | C2 | semidirect |
| 5. #19127937 | C2 | semidirect |
| 6. C2×#14581726 | C2 | semidirect |
| 7. #19127703 | C2 | semidirect |
| 8. C2×#131×C83 | C2 | semidirect |
| 56. C2×C8×C83 | D4 | semidirect |
| 109. C83 | #3061 | semidirect |
| 111. C2×#131 | D83 | semidirect |
| 160. C2×C8 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581814 | 2 |
| #19128279 | 2 |
| #19127947 | 2 |
| #19127942 | 2 |
| #19127937 | 2 |
| C2×#14581726 | 2 |
| #19127703 | 2 |
| C2×#131×C83 | 2 |
| #3061 | 83 |