Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
694 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 694 conjugacy classes of subgroups — too many to draw. Only its 169 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. #11722557 | C2 | direct (N × H) |
| 2. C2×#88683 | C2 | semidirect |
| 4. C2×C9×H(5,𝔽2) | C3 | semidirect |
| 5. C2×#63700 | C3 | semidirect |
| 7. #88683 | C22 | semidirect |
| 8. C2×C9⋊SL(2,𝔽3) | C22 | semidirect |
| 12. C9×H(5,𝔽2) | C2×C3 | semidirect |
| 16. #63700 | C2×C3 | semidirect |
| 20. C9⋊SL(2,𝔽3) | C23 | semidirect |
| 69. C2×H(5,𝔽2) | 3−1+2 | semidirect |
| 99. H(5,𝔽2) | C2×3−1+2 | semidirect |
| 125. C2×C9 | #994 | semidirect |
| 150. C9 | C2×#994 | semidirect |
| 179. C2 | #11722557 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722557 | 2 |
| C2×#88683 | 2 |
| C2×C3×#994 | 3 |
| C2×C9×H(5,𝔽2) | 3 |
| C2×#63700 | 3 |
| C2×Q8×3−1+2 | 4 |