Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
251 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 251 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 |
|---|---|---|
| 1. C32×Q8×C9 | C3 | semidirect |
| 2. #10619912 | C3 | semidirect |
| 3. #10619585 | C3 | semidirect |
| 4. #10619576 | C3 | semidirect |
| 5. #10619575 | C3 | semidirect |
| 6. #10619574 | C3 | semidirect |
| 33. C32×C9 | SL(2,𝔽3) | semidirect |
| 99. Q8 | #6908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×Q8×C9 | 3 |
| #10619912 | 3 |
| #10619585 | 3 |
| #10619576 | 3 |
| #10619575 | 3 |
| #10619574 | 3 |
| C2×#6908 | 4 |