Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
150 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 47 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. #107×D83 | C2 | semidirect |
| 3. #19127529 | C2 | semidirect |
| 4. #19127528 | C2 | semidirect |
| 5. #19127502 | C2 | semidirect |
| 6. (C2×D83)⋊C16 | C2 | semidirect |
| 7. #357×C83 | C2 | semidirect |
| 71. C83 | #2233 | semidirect |
| 77. #357 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19127934 | 2 |
| #107×D83 | 2 |
| #19127529 | 2 |
| #19127528 | 2 |
| #19127502 | 2 |
| (C2×D83)⋊C16 | 2 |
| #357×C83 | 2 |
| #2233 | 83 |