Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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×#14581737 | C2 | semidirect |
| 3. #19127942 | C2 | semidirect |
| 4. #19127503 | C2 | semidirect |
| 5. C22⋊C16×C83 | C2 | semidirect |
| 7. C2×Dic332 | C22 | semidirect |
| 13. #14581726 | C22 | semidirect |
| 16. C2×C16×C83 | C22 | semidirect |
| 55. C22×C83 | SD32 | semidirect |
| 72. C83 | #2187 | semidirect |
| 77. C22⋊C16 | D83 | semidirect |
| 86. C2×C16 | C2×D83 | semidirect |
| 131. C22 | #14581737 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D664 | 2 |
| C2×#14581737 | 2 |
| #19127942 | 2 |
| #19127503 | 2 |
| C22⋊C16×C83 | 2 |
| #2187 | 83 |