Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
696 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 696 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 |
|---|---|---|
| 1. C2×#14581780 | C2 | semidirect |
| 2. C2×#14581771 | C2 | semidirect |
| 4. #19127607 | C2 | semidirect |
| 5. #19127603 | C2 | semidirect |
| 6. #19127592 | C2 | semidirect |
| 7. #19127580 | C2 | semidirect |
| 8. #19127567 | C2 | semidirect |
| 9. C22×C42×C83 | C2 | semidirect |
| 63. C42×C83 | D4 | semidirect |
| 103. C22×C83 | #124 | semidirect |
| 129. C83 | #2850 | semidirect |
| 133. C22×C42 | D83 | semidirect |
| 192. C42 | C22⋊D83 | semidirect |
| 237. C22 | #14581780 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581780 | 2 |
| C2×#14581771 | 2 |
| C2×#14581766 | 2 |
| #19127607 | 2 |
| #19127603 | 2 |
| #19127592 | 2 |
| #19127580 | 2 |
| #19127567 | 2 |
| C22×C42×C83 | 2 |
| #2850 | 83 |