Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
632 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 95 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. C2×#88548 | C2 | semidirect |
| 3. C9×#946 | C2 | semidirect |
| 4. C2×C3×#3675 | C2 | semidirect |
| 5. (C2×D3)⋊(C9⋊C8) | C2 | semidirect |
| 6. #11720267 | C2 | semidirect |
| 7. #11720266 | C2 | semidirect |
| 11. C2×C3×Q8×C9 | C22 | semidirect |
| 19. C2×C3⋊(C9⋊C8) | C22 | semidirect |
| 22. C9×C4⋊Dic3 | C22 | semidirect |
| 24. C2×C3×C9⋊C8 | C22 | semidirect |
| 36. C2×#3675 | D3 | semidirect |
| 80. C2×Q8×C9 | C2×D3 | semidirect |
| 96. C2×C9⋊C8 | C2×D3 | semidirect |
| 103. C2×D3×C9 | SD16 | semidirect |
| 117. #946 | D9 | semidirect |
| 188. C2×C3×Q8 | C2×D9 | semidirect |
| 213. C4⋊Dic3 | C2×D9 | semidirect |
| 265. C3×C9 | #450 | semidirect |
| 333. C2×Q8 | D3×D9 | semidirect |
| 372. C2×D3 | #3675 | semidirect |
| 388. C9 | #5169 | semidirect |
| 443. C3 | #10588729 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×D36 | 2 |
| C2×#88548 | 2 |
| C9×#946 | 2 |
| C2×C3×#3675 | 2 |
| (C2×D3)⋊(C9⋊C8) | 2 |
| #11720267 | 2 |
| #11720266 | 2 |
| #10591651 | 3 |
| #10588729 | 3 |