Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
840 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 171 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. C3×C9×H(5,𝔽2) | C2 | semidirect |
| 2. #11721867 | C2 | semidirect |
| 3. #11721840 | C2 | semidirect |
| 4. #11720585 | C2 | semidirect |
| 5. #11720575 | C2 | semidirect |
| 14. C2×C4⋊(C3⋊D9) | C22 | semidirect |
| 17. C4×C3⋊Dic9 | C22 | semidirect |
| 18. #88532 | C22 | semidirect |
| 22. C9×H(5,𝔽2) | D3 | semidirect |
| 32. C3×Q8×C9 | D4 | semidirect |
| 36. C3×D4×C9 | D4 | semidirect |
| 78. C3×H(5,𝔽2) | D9 | semidirect |
| 106. Q8×C9 | #67 | semidirect |
| 110. D4×C9 | #67 | semidirect |
| 166. H(5,𝔽2) | C3⋊D9 | semidirect |
| 171. C3×C9 | #453 | semidirect |
| 178. C3×Q8 | #611 | semidirect |
| 186. C3×D4 | #611 | semidirect |
| 244. C9 | #5241 | semidirect |
| 248. Q8 | #6233 | semidirect |
| 254. D4 | #6233 | semidirect |
| 280. C3 | #10588922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×H(5,𝔽2) | 2 |
| #11721867 | 2 |
| #11721840 | 2 |
| #11720585 | 2 |
| #11720575 | 2 |
| #10592940 | 3 |
| #10588922 | 3 |