Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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. #19128169 | C2 | semidirect |
| 3. #19127812 | C2 | semidirect |
| 4. #19127807 | C2 | semidirect |
| 5. #19127800 | C2 | semidirect |
| 6. #19127695 | C2 | semidirect |
| 7. C2×#14581702 | C2 | semidirect |
| 8. #427×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 |
| 48. C2×C8×C83 | C2×C4 | semidirect |
| 90. C83 | #2943 | semidirect |
| 96. #427 | D83 | semidirect |
| 133. 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 |
| #19128169 | 2 |
| #19127812 | 2 |
| #19127807 | 2 |
| #19127800 | 2 |
| #19127695 | 2 |
| C2×#14581702 | 2 |
| #427×C83 | 2 |
| #2943 | 83 |