Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
160 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 49 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×#14581737 | C2 | semidirect |
| 2. C2×#14581731 | C2 | semidirect |
| 3. #19127943 | C2 | semidirect |
| 5. #19127504 | C2 | semidirect |
| 6. #19127501 | C2 | semidirect |
| 7. #366×C83 | C2 | semidirect |
| 39. C16×C83 | D4 | semidirect |
| 76. C83 | #2220 | semidirect |
| 81. #366 | D83 | semidirect |
| 115. C16 | D332 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581737 | 2 |
| C2×#14581731 | 2 |
| #19127943 | 2 |
| #19127938 | 2 |
| #19127504 | 2 |
| #19127501 | 2 |
| #366×C83 | 2 |
| #2220 | 83 |