Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2772 conjugacy classes of subgroups; only the 571 normal subgroups are shown.
This group has 2772 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×D4 | C2 | semidirect |
| 2. C2×#88860 | C2 | semidirect |
| 3. #11723971 | C2 | semidirect |
| 4. #11722202 | C2 | semidirect |
| 5. #11722200 | C2 | semidirect |
| 13. C2×C4⋊(C3⋊(C3⋊D3)) | C22 | semidirect |
| 16. C4⋊(C3⋊(C3⋊Dic3)) | C22 | semidirect |
| 17. C2×C3⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 18. C22×C32×D4 | D3 | semidirect |
| 31. C33×D4 | D4 | semidirect |
| 57. C22×C33 | D8 | semidirect |
| 65. C22×C3×D4 | C3⋊D3 | semidirect |
| 78. C32×D4 | #67 | semidirect |
| 110. C22×C32 | #213 | semidirect |
| 118. C22×D4 | C3⋊(C3⋊D3) | semidirect |
| 123. C33 | #447 | semidirect |
| 132. C3×D4 | #638 | semidirect |
| 163. C22×C3 | #3753 | semidirect |
| 171. C32 | #5217 | semidirect |
| 182. D4 | #6312 | semidirect |
| 203. C22 | #88860 | semidirect |
| 208. C3 | #10592916 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C33×D4 | 2 |
| C2×#88860 | 2 |
| #11723971 | 2 |
| #11722202 | 2 |
| #11722200 | 2 |
| #10592916 | 3 |