Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
596 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 171 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×#88399 | C2 | semidirect |
| 2. C22×D108 | C2 | semidirect |
| 3. C2×M16×C27 | C2 | semidirect |
| 4. #11720157 | C2 | direct (N × H) |
| 5. C2×D216 | C2 | semidirect |
| 6. C2×#88360 | C2 | semidirect |
| 12. #88399 | C22 | semidirect |
| 16. C2×D108 | C22 | semidirect |
| 17. C2×D108 | C22 | semidirect |
| 19. C2×Dic54 | C22 | semidirect |
| 20. M16×C27 | C22 | semidirect |
| 21. C2×C8×C27 | C22 | semidirect |
| 22. D216 | C22 | semidirect |
| 23. #88360 | C22 | semidirect |
| 45. D108 | C23 | semidirect |
| 48. Dic54 | C23 | semidirect |
| 49. C8×C27 | C23 | semidirect |
| 107. C2×C27 | AGL(1,ℤ/8) | semidirect |
| 144. C2×M16 | D27 | semidirect |
| 145. C27 | C2×AGL(1,ℤ/8) | semidirect |
| 185. M16 | C2×D27 | semidirect |
| 186. C2×C8 | C2×D27 | semidirect |
| 219. C8 | C22×D27 | semidirect |
| 241. C2 | #11720157 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88399 | 2 |
| C22×D108 | 2 |
| C2×M16×C27 | 2 |
| #11720157 | 2 |
| C2×D216 | 2 |
| C2×#88360 | 2 |
| C2×#63470 | 3 |