Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
220 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 75 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×#14581731 | C2 | semidirect |
| 3. M32×D83 | C2 | semidirect |
| 4. #19127486 | C2 | semidirect |
| 5. #19127485 | C2 | semidirect |
| 6. #19127484 | C2 | semidirect |
| 7. #350×C83 | C2 | semidirect |
| 18. #14581732 | C22 | semidirect |
| 22. C2×C83⋊C16 | C22 | semidirect |
| 25. M32×C83 | C22 | semidirect |
| 26. C2×C16×C83 | C22 | semidirect |
| 109. C83 | #2117 | semidirect |
| 116. #350 | D83 | semidirect |
| 132. M32 | C2×D83 | semidirect |
| 135. C2×C16 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #131×D83 | 2 |
| C2×#14581731 | 2 |
| M32×D83 | 2 |
| #19127486 | 2 |
| #19127485 | 2 |
| #19127484 | 2 |
| #350×C83 | 2 |
| #2117 | 83 |