Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1736 conjugacy classes of subgroups; only the 407 normal subgroups are shown.
This group has 1736 conjugacy classes of subgroups — too many to draw. Only its 407 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×SD16 | C2 | semidirect |
| 2. #11723987 | C2 | semidirect |
| 4. C2×C8×C3⋊(C3⋊D3) | C2 | semidirect |
| 5. #11722205 | C2 | semidirect |
| 6. #11722202 | C2 | semidirect |
| 7. #11722187 | C2 | semidirect |
| 22. C2×C32×SD16 | D3 | semidirect |
| 43. C33×C8 | D4 | semidirect |
| 65. C2×C3⋊(C3⋊D3) | SD16 | semidirect |
| 72. C2×C3×SD16 | C3⋊D3 | semidirect |
| 93. C32×C8 | #67 | semidirect |
| 127. C2×SD16 | C3⋊(C3⋊D3) | semidirect |
| 134. C33 | #465 | semidirect |
| 149. C3×C8 | #638 | semidirect |
| 182. C32 | #5171 | semidirect |
| 198. C8 | #6312 | semidirect |
| 217. C3 | #10592870 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×SD16 | 2 |
| #11723987 | 2 |
| #11723979 | 2 |
| C2×C8×C3⋊(C3⋊D3) | 2 |
| #11722205 | 2 |
| #11722202 | 2 |
| #11722187 | 2 |
| #10592870 | 3 |