Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
534 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 1. C22×#6895 | C2 | semidirect |
| 2. C2×#6895⋊C2 | C2 | direct (N × H) |
| 6. C2×#6895 | C22 | semidirect |
| 7. #6895⋊C2 | C22 | direct (N × H) |
| 11. C22×C9⋊C9 | D3 | semidirect |
| 16. #6895 | C23 | semidirect |
| 24. C2×C9⋊C9 | C2×D3 | semidirect |
| 41. C9⋊C9 | C22×D3 | semidirect |
| 118. C22 | #6895⋊C2 | direct (N × H) |
| 124. C2 | C2×#6895⋊C2 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6895 | 2 |
| C2×#6895⋊C2 | 2 |
| C22×C9×C3⋊D3 | 3 |
| C22×#4181 | 3 |
| C22×D9⋊C9 | 3 |