Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
408 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 113 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×C22⋊(C83⋊C8) | C2 | semidirect |
| 3. C2×(C2×D83)⋊C8 | C2 | semidirect |
| 4. #19127455 | C2 | semidirect |
| 5. C22×M16×C83 | C2 | semidirect |
| 50. C2×C8×C83 | D4 | semidirect |
| 61. C22×D83 | M16 | semidirect |
| 78. C2×Dic83 | M16 | semidirect |
| 114. C83 | #1870 | semidirect |
| 115. C22×M16 | D83 | semidirect |
| 159. C2×C8 | C22⋊D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊D83 | 2 |
| C2×C22⋊(C83⋊C8) | 2 |
| C2×(C2×D83)⋊C8 | 2 |
| #19127455 | 2 |
| C22×M16×C83 | 2 |
| #1870 | 83 |