Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1148 conjugacy classes of subgroups; only the 403 normal subgroups are shown.
This group has 1148 conjugacy classes of subgroups — too many to draw. Only its 403 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 |
|---|---|---|
| 3. #11722199 | C2 | direct (N × H) |
| 55. C2×C33 | Q32 | semidirect |
| 74. C33 | C2×Q32 | semidirect |
| 84. C2×C32 | #829 | semidirect |
| 99. C32 | C2×#829 | semidirect |
| 109. C2×C3 | #63656 | semidirect |
| 116. C3 | C2×#63656 | semidirect |
| 117. C2 | #11722199 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×Q16 | 2 |
| C2×#88853 | 2 |
| #11722199 | 2 |
| C2×C3⋊(C3⋊(C3⋊C16)) | 2 |
| C2×#63656 | 3 |