Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
452 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 452 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×#88548 | C2 | semidirect |
| 2. Q8×C9×Dic3 | C2 | semidirect |
| 3. C2×C3×#3675 | C2 | semidirect |
| 5. #11720267 | C2 | semidirect |
| 6. #11720266 | C2 | semidirect |
| 7. Dic3⋊(C9⋊C8) | C2 | semidirect |
| 33. C2×#3675 | D3 | semidirect |
| 41. C3×Q8×C9 | D4 | semidirect |
| 99. C9×Dic3 | SD16 | semidirect |
| 102. Q8×Dic3 | D9 | semidirect |
| 138. Q8×C9 | #67 | semidirect |
| 233. C3×C9 | #460 | semidirect |
| 243. C3×Q8 | D36 | semidirect |
| 335. Dic3 | #3675 | semidirect |
| 338. C9 | #5163 | semidirect |
| 342. Q8 | #6192 | semidirect |
| 384. C3 | #10588710 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88548 | 2 |
| Q8×C9×Dic3 | 2 |
| C2×C3×#3675 | 2 |
| #11721006 | 2 |
| #11720267 | 2 |
| #11720266 | 2 |
| Dic3⋊(C9⋊C8) | 2 |
| #10591617 | 3 |
| #10588710 | 3 |