Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2772 conjugacy classes of subgroups; only the 463 normal subgroups are shown.
This group has 2772 conjugacy classes of subgroups — too many to draw. Only its 463 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. C22×C4⋊(C3⋊(C3⋊D3)) | C2 | semidirect |
| 2. C33×#121 | C2 | semidirect |
| 3. C2×#88860 | C2 | semidirect |
| 4. #11722200 | C2 | semidirect |
| 5. #11722179 | C2 | semidirect |
| 9. C2×C33×D4 | C22 | semidirect |
| 14. C33×C4⋊C4 | C22 | semidirect |
| 17. C2×C3⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 19. C32×#121 | D3 | semidirect |
| 37. C4⋊(C3⋊(C3⋊D3)) | D4 | semidirect |
| 42. C2×C32×D4 | C2×D3 | semidirect |
| 47. C32×C4⋊C4 | C2×D3 | semidirect |
| 56. C22×C33 | D8 | semidirect |
| 66. C3×#121 | C3⋊D3 | semidirect |
| 95. C2×C3×D4 | C2×C3⋊D3 | semidirect |
| 100. C3×C4⋊C4 | C2×C3⋊D3 | semidirect |
| 109. C22×C32 | #213 | semidirect |
| 120. #121 | C3⋊(C3⋊D3) | semidirect |
| 123. C33 | #447 | semidirect |
| 151. C2×D4 | C2×C3⋊(C3⋊D3) | semidirect |
| 155. C4⋊C4 | C2×C3⋊(C3⋊D3) | semidirect |
| 162. C22×C3 | #3753 | semidirect |
| 171. C32 | #5036 | semidirect |
| 203. C22 | #88860 | semidirect |
| 208. C3 | #10592735 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊(C3⋊(C3⋊D3)) | 2 |
| C33×#121 | 2 |
| C2×#88860 | 2 |
| #11722200 | 2 |
| #11722179 | 2 |
| #10592735 | 3 |