Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
308 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 59 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. #19128049 | C2 | semidirect |
| 3. #19127903 | C2 | semidirect |
| 4. #19127444 | C2 | semidirect |
| 5. D4⋊(C83⋊C8) | C2 | semidirect |
| 6. #19127428 | C2 | semidirect |
| 7. #474×C83 | C2 | semidirect |
| 16. C4⋊(C83⋊C8) | C22 | semidirect |
| 19. C4×C83⋊C8 | C22 | semidirect |
| 20. C4⋊Q8×C83 | C22 | semidirect |
| 23. C4⋊C8×C83 | C22 | semidirect |
| 61. D4×C83 | SD16 | semidirect |
| 110. C83 | #1639 | semidirect |
| 113. #474 | D83 | semidirect |
| 121. C4⋊Q8 | C2×D83 | semidirect |
| 130. C4⋊C8 | C2×D83 | semidirect |
| 180. D4 | #13050577 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×D332 | 2 |
| #19128049 | 2 |
| #19127903 | 2 |
| #19127444 | 2 |
| D4⋊(C83⋊C8) | 2 |
| #19127428 | 2 |
| #474×C83 | 2 |
| #1639 | 83 |