Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
436 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 161 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 |
|---|---|---|
| 3. C2×C8×Dic83 | C2 | semidirect |
| 4. #19127456 | C2 | semidirect |
| 5. #336×C83 | C2 | semidirect |
| 12. (C2×D83)⋊C8 | C4 | semidirect |
| 24. C2×C4×D83 | C8 | semidirect |
| 28. C2×C83⋊C8 | C2×C4 | semidirect |
| 35. C2×C8×C83 | C2×C4 | semidirect |
| 70. C2×D83 | C4×C8 | semidirect |
| 75. Dic83 | C22⋊C8 | semidirect |
| 83. C83 | C4×C22⋊C8 | semidirect |
| 88. #336 | D83 | semidirect |
| 116. C2×C8 | C4×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D83 | 2 |
| C2×(C2×D83)⋊C8 | 2 |
| C2×C8×Dic83 | 2 |
| #19127456 | 2 |
| #336×C83 | 2 |
| C4×C22⋊C8 | 83 |