Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1596 conjugacy classes of subgroups; only the 459 normal subgroups are shown.
This group has 1596 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. C2×C33×C4⋊C4 | C2 | semidirect |
| 3. #11722200 | C2 | semidirect |
| 4. #11722179 | C2 | semidirect |
| 5. #11722178 | C2 | semidirect |
| 16. C2×C32×C4⋊C4 | D3 | semidirect |
| 53. C2×C3×C4⋊C4 | C3⋊D3 | semidirect |
| 96. C2×C4⋊C4 | C3⋊(C3⋊D3) | semidirect |
| 100. C33 | #481 | semidirect |
| 137. C32 | #4968 | semidirect |
| 165. C3 | #10592667 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×C4⋊C4 | 2 |
| #11723971 | 2 |
| #11722200 | 2 |
| #11722179 | 2 |
| #11722178 | 2 |
| #10592667 | 3 |