Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
248 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. C22×C27⋊C8 | C2 | semidirect |
| 3. C2×#88359 | C2 | semidirect |
| 4. C27×C22⋊C8 | C2 | semidirect |
| 5. (C2×D27)⋊C8 | C2 | semidirect |
| 6. #11720056 | C2 | semidirect |
| 7. Dic27⋊C8 | C2 | semidirect |
| 44. C27⋊C8 | D4 | semidirect |
| 61. C22×C27 | M16 | semidirect |
| 132. C22⋊C8 | D27 | semidirect |
| 134. C27 | #435 | semidirect |
| 209. C22 | #88359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6171 | 2 |
| C22×C27⋊C8 | 2 |
| C2×#88359 | 2 |
| C27×C22⋊C8 | 2 |
| (C2×D27)⋊C8 | 2 |
| #11720056 | 2 |
| Dic27⋊C8 | 2 |
| #10588412 | 3 |