Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
368 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 85 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×#14581723 | C2 | semidirect |
| 3. C2×#14581713 | C2 | semidirect |
| 4. C2×(C2×D83)⋊C8 | C2 | semidirect |
| 5. #19127558 | C2 | semidirect |
| 6. #19127464 | C2 | semidirect |
| 7. C2×#102×C83 | C2 | semidirect |
| 40. C2×C83⋊C8 | D4 | semidirect |
| 144. C83 | #2034 | semidirect |
| 148. C2×#102 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581763 | 2 |
| C2×#14581723 | 2 |
| C2×#14581713 | 2 |
| C2×(C2×D83)⋊C8 | 2 |
| #19127558 | 2 |
| #19127464 | 2 |
| C2×#102×C83 | 2 |
| #2034 | 83 |