Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 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. #19128073 | C2 | semidirect |
| 2. #19127981 | C2 | semidirect |
| 3. D4×C83⋊C8 | C2 | semidirect |
| 4. #19127451 | C2 | semidirect |
| 5. #19127446 | C2 | semidirect |
| 6. #19127445 | C2 | semidirect |
| 51. D4×C83 | SD16 | semidirect |
| 65. C83⋊C8 | D8 | semidirect |
| 86. C83 | #1665 | semidirect |
| 139. D4 | #13050578 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128073 | 2 |
| #19127981 | 2 |
| D4×C83⋊C8 | 2 |
| #19127451 | 2 |
| #19127446 | 2 |
| #19127445 | 2 |
| #459×C83 | 2 |
| #1665 | 83 |