Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
524 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 163 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. C2×M16×C27 | C2 | semidirect |
| 3. #11720158 | C2 | semidirect |
| 4. #11720157 | C2 | semidirect |
| 5. #11720154 | C2 | semidirect |
| 12. #88399 | C22 | semidirect |
| 13. C2×D108 | C22 | semidirect |
| 15. C2×Dic54 | C22 | semidirect |
| 16. M16×C27 | C22 | semidirect |
| 17. C2×C8×C27 | C22 | semidirect |
| 18. D216 | C22 | semidirect |
| 19. #88360 | C22 | semidirect |
| 20. Dic108 | C22 | semidirect |
| 119. C2×M16 | D27 | semidirect |
| 120. C27 | #575 | semidirect |
| 153. M16 | C2×D27 | semidirect |
| 154. C2×C8 | C2×D27 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88399 | 2 |
| C2×M16×C27 | 2 |
| #11720158 | 2 |
| #11720157 | 2 |
| #11720154 | 2 |
| #10589850 | 3 |