Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 125 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. #19128373 | C2 | semidirect |
| 2. #19128067 | C2 | semidirect |
| 3. #19128049 | C2 | semidirect |
| 4. #19127998 | C2 | semidirect |
| 5. #19127988 | C2 | semidirect |
| 6. #19127896 | C2 | semidirect |
| 7. #19127896 | C2 | semidirect |
| 8. #19127832 | C2 | semidirect |
| 9. #19127811 | C2 | semidirect |
| 10. C4×#13050575 | C2 | semidirect |
| 11. #554×C83 | C2 | semidirect |
| 80. D4×C83 | #41 | semidirect |
| 130. C83 | #3366 | semidirect |
| 131. #554 | D83 | semidirect |
| 218. D4 | #13050591 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128373 | 2 |
| #19128067 | 2 |
| #19128049 | 2 |
| #19127998 | 2 |
| #19127988 | 2 |
| #19127896 | 2 |
| #19127832 | 2 |
| #19127811 | 2 |
| C4×#13050575 | 2 |
| #554×C83 | 2 |
| #3366 | 83 |