Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
166 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 55 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. C4⋊(C83⋊C16) | C2 | semidirect |
| 4. #19127505 | C2 | semidirect |
| 5. #494×C83 | C2 | semidirect |
| 52. C4×C83 | SD32 | semidirect |
| 61. C83 | #2208 | semidirect |
| 63. #494 | D83 | semidirect |
| 114. C4 | #14581735 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581735 | 2 |
| C4×D664 | 2 |
| C4⋊(C83⋊C16) | 2 |
| #19127505 | 2 |
| #494×C83 | 2 |
| #2208 | 83 |