Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
816 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 349 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 |
|---|---|---|
| 3. C2×#14581715 | C2 | direct (N × H) |
| 7. C22×Dic166 | C4 | semidirect |
| 12. #14581715 | C22 | direct (N × H) |
| 20. C2×Dic166 | C2×C4 | semidirect |
| 50. Dic166 | C22×C4 | semidirect |
| 52. C22×C83 | #103 | semidirect |
| 62. C2×C83 | C2×#103 | semidirect |
| 67. C83 | C22×#103 | semidirect |
| 119. C22 | #14581715 | direct (N × H) |
| 129. C2 | C2×#14581715 | 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 |
| C23×C83⋊C8 | 2 |
| C2×#14581715 | 2 |
| C22×C4⋊C4×C83 | 2 |
| C22×#103 | 83 |