Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
292 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#14581728 | C2 | semidirect |
| 3. C2×#14581720 | C2 | semidirect |
| 4. #19127667 | C2 | semidirect |
| 5. C2×#97×C83 | C2 | semidirect |
| 9. C2×Dic332 | C4 | semidirect |
| 10. C2×#13050579 | C4 | semidirect |
| 11. C2×D664 | C4 | semidirect |
| 86. C83 | #1975 | semidirect |
| 91. C2×#97 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581814 | 2 |
| C2×#14581728 | 2 |
| C2×#14581720 | 2 |
| #19127667 | 2 |
| C2×#97×C83 | 2 |
| #1975 | 83 |