Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
1464 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 565 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. C23×Dic166 | C2 | semidirect |
| 2. C2×#14581822 | C2 | direct (N × H) |
| 3. C22×#13050580 | C2 | semidirect |
| 4. C22×#13050578 | C2 | semidirect |
| 5. C22×#13050574 | C2 | semidirect |
| 10. C22×Dic166 | C22 | semidirect |
| 12. #14581822 | C22 | direct (N × H) |
| 13. C2×#13050580 | C22 | semidirect |
| 14. C2×#13050578 | C22 | semidirect |
| 15. C2×#13050574 | C22 | semidirect |
| 28. C2×Dic166 | C23 | semidirect |
| 31. #13050580 | C23 | semidirect |
| 32. #13050578 | C23 | semidirect |
| 33. #13050574 | C23 | semidirect |
| 76. C22×C83 | #137 | semidirect |
| 86. C2×C83 | C2×#137 | semidirect |
| 89. C83 | C22×#137 | semidirect |
| 165. C22 | #14581822 | direct (N × H) |
| 175. C2 | C2×#14581822 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic166 | 2 |
| C2×#14581822 | 2 |
| C22×#13050580 | 2 |
| C22×#13050578 | 2 |
| C22×#13050574 | 2 |
| C22×#41×C83 | 2 |
| C22×#137 | 83 |