Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
184 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 51 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. #19127902 | C2 | semidirect |
| 3. #19127898 | C2 | semidirect |
| 4. #19127828 | C2 | semidirect |
| 5. #19127451 | C2 | semidirect |
| 6. #19127444 | C2 | semidirect |
| 7. #331×C83 | C2 | semidirect |
| 66. C83⋊C8 | SD16 | semidirect |
| 87. C83 | #1688 | semidirect |
| 94. #331 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128077 | 2 |
| #19127902 | 2 |
| #19127898 | 2 |
| #19127828 | 2 |
| #19127451 | 2 |
| #19127444 | 2 |
| #331×C83 | 2 |
| #1688 | 83 |