Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
256 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 57 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. C2×#14581735 | C2 | semidirect |
| 3. #19127501 | C2 | semidirect |
| 4. C22⋊(C83⋊C16) | C2 | semidirect |
| 5. #467×C83 | C2 | semidirect |
| 11. C2×C83⋊C16 | C22 | semidirect |
| 12. C2×Q16×C83 | C22 | semidirect |
| 15. #107×C83 | C22 | semidirect |
| 55. C22×C83 | SD32 | semidirect |
| 72. C83 | #2187 | semidirect |
| 75. #467 | D83 | semidirect |
| 79. C2×Q16 | C2×D83 | semidirect |
| 87. #107 | C2×D83 | semidirect |
| 131. C22 | #14581735 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D664 | 2 |
| C2×#14581735 | 2 |
| #19127501 | 2 |
| C22⋊(C83⋊C16) | 2 |
| #467×C83 | 2 |
| #2187 | 83 |