Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
512 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 309 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. #19127739 | C2 | direct (N × H) |
| 3. C2×#14581726 | C2 | semidirect |
| 4. C2×#14581724 | C2 | semidirect |
| 11. #14581726 | C22 | semidirect |
| 12. #14581724 | C22 | semidirect |
| 14. C22×C8×C83 | C4 | semidirect |
| 32. C2×C8×C83 | C2×C4 | semidirect |
| 64. C2×C83 | #427 | semidirect |
| 68. C83 | C2×#427 | semidirect |
| 75. C22×C8 | Dic83 | semidirect |
| 96. C2×C8 | C2×Dic83 | semidirect |
| 132. C2 | #19127739 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581751 | 2 |
| #19127739 | 2 |
| C2×#14581726 | 2 |
| C2×#14581724 | 2 |
| C23×C8×C83 | 2 |
| C2×#427 | 83 |