Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
300 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 83 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×#14581727 | C2 | semidirect |
| 3. C2×#14581720 | C2 | semidirect |
| 4. #19127669 | C2 | semidirect |
| 5. #19127668 | C2 | semidirect |
| 6. C2×C4×C83⋊C8 | C2 | semidirect |
| 7. C2×#104×C83 | C2 | semidirect |
| 11. C2×#13050580 | C4 | semidirect |
| 12. C2×#13050578 | C4 | semidirect |
| 13. C2×#13050577 | C4 | semidirect |
| 14. C2×#13050575 | C4 | semidirect |
| 120. C83 | #1974 | semidirect |
| 124. C2×#104 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581812 | 2 |
| C2×#14581727 | 2 |
| C2×#14581720 | 2 |
| #19127669 | 2 |
| #19127668 | 2 |
| C2×C4×C83⋊C8 | 2 |
| C2×#104×C83 | 2 |
| #1974 | 83 |