Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
552 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14581824 | C2 | semidirect |
| 2. C2×#14581821 | C2 | semidirect |
| 4. C4⋊Q8×D83 | C2 | semidirect |
| 5. #19128096 | C2 | semidirect |
| 6. #19128095 | C2 | semidirect |
| 7. #19128093 | C2 | semidirect |
| 8. #19128079 | C2 | semidirect |
| 9. #19128072 | C2 | semidirect |
| 10. #19127653 | C2 | semidirect |
| 11. #497×C83 | C2 | semidirect |
| 63. #13050573 | D4 | semidirect |
| 124. Dic83 | #137 | semidirect |
| 131. C83 | #3152 | semidirect |
| 139. #497 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581824 | 2 |
| C2×#14581821 | 2 |
| #19128250 | 2 |
| C4⋊Q8×D83 | 2 |
| #19128096 | 2 |
| #19128095 | 2 |
| #19128093 | 2 |
| #19128079 | 2 |
| #19128072 | 2 |
| #19127653 | 2 |
| #497×C83 | 2 |
| #3152 | 83 |