Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
484 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 484 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. C2×#14581800 | C2 | semidirect |
| 3. #19128282 | C2 | semidirect |
| 4. #19128279 | C2 | semidirect |
| 5. #19127958 | C2 | semidirect |
| 6. #19127953 | C2 | semidirect |
| 7. #19127933 | C2 | semidirect |
| 8. #19127929 | C2 | semidirect |
| 9. C2×#14581723 | C2 | semidirect |
| 10. #19127703 | C2 | semidirect |
| 11. #417×C83 | C2 | semidirect |
| 63. C2×C83⋊C8 | D4 | semidirect |
| 153. C83 | #3060 | semidirect |
| 164. #417 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581812 | 2 |
| C2×#14581800 | 2 |
| #19128282 | 2 |
| #19128279 | 2 |
| #19127958 | 2 |
| #19127953 | 2 |
| #19127933 | 2 |
| #19127929 | 2 |
| C2×#14581723 | 2 |
| #19127703 | 2 |
| #417×C83 | 2 |
| #3060 | 83 |