Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2772 conjugacy classes of subgroups; only the 459 normal subgroups are shown.
This group has 2772 conjugacy classes of subgroups — too many to draw. Only its 459 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. C33×H(5,𝔽2) | C2 | semidirect |
| 2. #11723978 | C2 | semidirect |
| 3. #11722204 | C2 | semidirect |
| 5. C23×C3⋊(C3⋊D3) | C22 | semidirect |
| 10. #88864 | C22 | semidirect |
| 12. C32×H(5,𝔽2) | D3 | semidirect |
| 16. C23×C33 | D4 | semidirect |
| 24. C2×C33×C4 | D4 | semidirect |
| 45. C3×H(5,𝔽2) | C3⋊D3 | semidirect |
| 49. C23×C32 | #67 | semidirect |
| 57. C2×C32×C4 | #67 | semidirect |
| 82. H(5,𝔽2) | C3⋊(C3⋊D3) | semidirect |
| 85. C33 | B(4,𝔽2) | semidirect |
| 87. C23×C3 | #638 | semidirect |
| 95. C2×C3×C4 | #638 | semidirect |
| 119. C32 | #5244 | semidirect |
| 123. C23 | #6312 | semidirect |
| 131. C2×C4 | #6312 | semidirect |
| 146. C3 | #10592943 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×H(5,𝔽2) | 2 |
| #11723978 | 2 |
| #11722204 | 2 |
| #10592943 | 3 |