Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
230 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 53 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×#14581814 | C2 | semidirect |
| 2. C2×#14581736 | C2 | semidirect |
| 3. C2×#14581733 | C2 | semidirect |
| 4. #19127504 | C2 | semidirect |
| 5. #19127501 | C2 | semidirect |
| 6. C22⋊(C83⋊C16) | C2 | semidirect |
| 7. #466×C83 | C2 | semidirect |
| 30. Dic332 | D4 | semidirect |
| 33. D664 | D4 | semidirect |
| 90. C83 | #2186 | semidirect |
| 94. #466 | 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×#14581736 | 2 |
| C2×#14581733 | 2 |
| #19127504 | 2 |
| #19127501 | 2 |
| C22⋊(C83⋊C16) | 2 |
| #466×C83 | 2 |
| #2186 | 83 |