Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14581812 | C2 | semidirect |
| 2. #19128372 | C2 | semidirect |
| 3. #19128077 | C2 | semidirect |
| 4. #19127935 | C2 | semidirect |
| 5. #19127901 | C2 | semidirect |
| 6. #19127898 | C2 | semidirect |
| 7. #19127846 | C2 | semidirect |
| 8. #19127844 | C2 | semidirect |
| 9. C4×#13050580 | C2 | semidirect |
| 10. D4×C83⋊C8 | C2 | semidirect |
| 11. #550×C83 | C2 | semidirect |
| 51. #13050580 | D4 | semidirect |
| 131. C4×C83 | #135 | semidirect |
| 143. C83 | #3287 | semidirect |
| 146. #550 | D83 | semidirect |
| 276. C4 | #14581812 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581812 | 2 |
| #19128372 | 2 |
| #19128077 | 2 |
| #19127935 | 2 |
| #19127901 | 2 |
| #19127898 | 2 |
| #19127846 | 2 |
| #19127844 | 2 |
| C4×#13050580 | 2 |
| D4×C83⋊C8 | 2 |
| #550×C83 | 2 |
| #3287 | 83 |