Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
199 conjugacy classes of subgroups; only the 33 normal subgroups are shown.
This group has 199 conjugacy classes of subgroups — too many to draw. Only its 33 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×#41⋊C27 | C2 | semidirect |
| 2. C2×#88391 | C2 | semidirect |
| 3. #11720108 | C2 | semidirect |
| 19. Q8⋊C27 | D4 | semidirect |
| 94. C2×#41 | D27 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41⋊C27 | 2 |
| C2×#88391 | 2 |
| #11720108 | 2 |
| #10588919 | 3 |
| (C2×D27)⋊C4 | 4 |