Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
368 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 40 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. #11757452 | C2 | direct (N × H) |
| 3. C2×C32⋊(C22⋊C9) | C3 | semidirect |
| 4. C2×C32⋊(C22⋊C9) | C3 | semidirect |
| 9. C32⋊(C22⋊C9) | C2×C3 | semidirect |
| 10. C32⋊(C22⋊C9) | C2×C3 | semidirect |
| 136. C23 | #6859 | semidirect |
| 154. C22 | C2×#6859 | semidirect |
| 162. C2 | #11757452 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11757452 | 2 |
| C23×C3×H(3,𝔽3) | 3 |
| C2×C32⋊(C22⋊C9) | 3 |
| C2×#6859 | 4 |