Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
484 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 189 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. #19128181 | C2 | semidirect |
| 3. #19127803 | C2 | semidirect |
| 4. C4×Dic332 | C2 | semidirect |
| 5. C4×D664 | C2 | semidirect |
| 6. C2×#14581726 | C2 | semidirect |
| 7. #19127703 | C2 | semidirect |
| 8. #405×C83 | C2 | semidirect |
| 10. #14581814 | C4 | semidirect |
| 30. #13050590 | C2×C4 | semidirect |
| 37. Dic332 | C2×C4 | semidirect |
| 38. #13050579 | C2×C4 | semidirect |
| 39. D664 | C2×C4 | semidirect |
| 47. C2×C8×C83 | C2×C4 | semidirect |
| 96. C83 | #2951 | semidirect |
| 104. #405 | D83 | semidirect |
| 138. 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×#14581814 | 2 |
| #19128181 | 2 |
| #19127803 | 2 |
| C4×Dic332 | 2 |
| C4×D664 | 2 |
| C2×#14581726 | 2 |
| #19127703 | 2 |
| #405×C83 | 2 |
| #2951 | 83 |