Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2212 conjugacy classes of subgroups; only the 571 normal subgroups are shown.
This group has 2212 conjugacy classes of subgroups — too many to draw. Only its 571 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×C33×Q8 | C2 | semidirect |
| 2. C2×#88862 | C2 | semidirect |
| 4. #11722205 | C2 | semidirect |
| 5. #11722200 | C2 | semidirect |
| 18. C22×C32×Q8 | D3 | semidirect |
| 27. C33×Q8 | D4 | semidirect |
| 51. C22×C33 | SD16 | semidirect |
| 60. C22×C3×Q8 | C3⋊D3 | semidirect |
| 69. C32×Q8 | #67 | semidirect |
| 98. C22×C32 | #215 | semidirect |
| 107. C22×Q8 | C3⋊(C3⋊D3) | semidirect |
| 112. C33 | #448 | semidirect |
| 117. C3×Q8 | #638 | semidirect |
| 145. C22×C3 | #3755 | semidirect |
| 154. C32 | #5227 | semidirect |
| 159. Q8 | #6312 | semidirect |
| 179. C22 | #88862 | semidirect |
| 185. C3 | #10592926 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C33×Q8 | 2 |
| C2×#88862 | 2 |
| #11723971 | 2 |
| #11722205 | 2 |
| #11722200 | 2 |
| #10592926 | 3 |