Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
532 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 532 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×C8×C27 | C2 | semidirect |
| 3. #11720154 | C2 | direct (N × H) |
| 4. C2×D216 | C2 | semidirect |
| 5. C2×#88360 | C2 | semidirect |
| 6. C2×Dic108 | C2 | semidirect |
| 11. #88399 | C22 | semidirect |
| 17. C2×C8×C27 | C22 | semidirect |
| 18. D216 | C22 | semidirect |
| 19. #88360 | C22 | semidirect |
| 20. Dic108 | C22 | semidirect |
| 88. C2×C27 | #135 | semidirect |
| 118. C22×C8 | D27 | semidirect |
| 119. C27 | C2×#135 | semidirect |
| 151. C2×C8 | C2×D27 | semidirect |
| 193. C2 | #11720154 | 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×C8×C27 | 2 |
| #11720154 | 2 |
| C2×D216 | 2 |
| C2×#88360 | 2 |
| C2×Dic108 | 2 |
| C2×#63467 | 3 |