Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
492 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 175 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. C4×#13050591 | C2 | semidirect |
| 3. #19127814 | C2 | semidirect |
| 4. #19127812 | C2 | semidirect |
| 5. #19127808 | C2 | semidirect |
| 6. #19127804 | C2 | semidirect |
| 7. #19127799 | C2 | semidirect |
| 8. #19127736 | C2 | semidirect |
| 9. #19127696 | C2 | semidirect |
| 10. #97×D83 | C2 | semidirect |
| 11. #441×C83 | C2 | semidirect |
| 13. #14581815 | C4 | semidirect |
| 41. #13050591 | C2×C4 | semidirect |
| 49. #13050577 | C2×C4 | semidirect |
| 50. D664 | C2×C4 | semidirect |
| 54. C8×D83 | C2×C4 | semidirect |
| 65. Q16×C83 | C2×C4 | semidirect |
| 115. C83 | #2943 | semidirect |
| 121. #441 | D83 | semidirect |
| 165. Q16 | C4×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581815 | 2 |
| C4×#13050591 | 2 |
| #19127814 | 2 |
| #19127812 | 2 |
| #19127808 | 2 |
| #19127804 | 2 |
| #19127799 | 2 |
| #19127736 | 2 |
| #19127696 | 2 |
| #97×D83 | 2 |
| #441×C83 | 2 |
| #2943 | 83 |