Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1736 conjugacy classes of subgroups; only the 415 normal subgroups are shown.
This group has 1736 conjugacy classes of subgroups — too many to draw. Only its 415 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. C2×#88850 | C2 | semidirect |
| 2. C2×C8×C3⋊(C3⋊D3) | C2 | semidirect |
| 4. C33×C4⋊C8 | C2 | semidirect |
| 5. #11722190 | C2 | semidirect |
| 6. #11722190 | C2 | semidirect |
| 7. #11722173 | C2 | semidirect |
| 25. C32×C4⋊C8 | D3 | semidirect |
| 44. C3⋊(C3⋊(C3⋊C8)) | D4 | semidirect |
| 65. C2×C3⋊(C3⋊D3) | M16 | semidirect |
| 75. C3×C4⋊C8 | C3⋊D3 | semidirect |
| 130. C4⋊C8 | C3⋊(C3⋊D3) | semidirect |
| 134. C33 | #435 | semidirect |
| 182. C32 | #4836 | semidirect |
| 217. C3 | #10592535 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88850 | 2 |
| C2×C8×C3⋊(C3⋊D3) | 2 |
| C4×C4⋊(C3⋊(C3⋊D3)) | 2 |
| C33×C4⋊C8 | 2 |
| #11722190 | 2 |
| #11722173 | 2 |
| #10592535 | 3 |