Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
368 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 89 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×#14581726 | C2 | semidirect |
| 3. C2×#14581714 | C2 | semidirect |
| 4. C2×#14581714 | C2 | semidirect |
| 5. #19127561 | C2 | semidirect |
| 6. #19127464 | C2 | semidirect |
| 7. C2×C22⋊C8×C83 | C2 | semidirect |
| 60. C2×C8×C83 | D4 | semidirect |
| 144. C83 | #2033 | semidirect |
| 149. C2×C22⋊C8 | D83 | semidirect |
| 196. 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×#14581766 | 2 |
| C2×#14581726 | 2 |
| C2×#14581714 | 2 |
| #19127561 | 2 |
| #19127464 | 2 |
| C2×C22⋊C8×C83 | 2 |
| #2033 | 83 |