Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
500 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 101 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×#88524 | C2 | semidirect |
| 2. C2×C3×D72 | C2 | semidirect |
| 3. #11721006 | C2 | semidirect |
| 4. #11720948 | C2 | semidirect |
| 5. C2×#88417 | C2 | semidirect |
| 6. C2×#88415 | C2 | semidirect |
| 7. C9×#815 | C2 | semidirect |
| 31. C2×D72 | D3 | semidirect |
| 53. C3×C8×C9 | D4 | semidirect |
| 54. C9×C3⋊C8 | D4 | semidirect |
| 112. #815 | D9 | semidirect |
| 154. C8×C9 | #67 | semidirect |
| 226. C3×C9 | #496 | semidirect |
| 266. C3×C8 | D36 | semidirect |
| 268. C3⋊C8 | D36 | semidirect |
| 325. C9 | #5154 | semidirect |
| 342. C8 | #6192 | semidirect |
| 368. C3 | #10588393 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88524 | 2 |
| C2×C3×D72 | 2 |
| #11721006 | 2 |
| #11720948 | 2 |
| C2×#88417 | 2 |
| C2×#88415 | 2 |
| C9×#815 | 2 |
| #10590883 | 3 |
| #10588393 | 3 |