Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
400 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 105 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. C4×C9×Dic6 | C2 | semidirect |
| 4. #11720516 | C2 | semidirect |
| 5. #11720297 | C2 | semidirect |
| 7. #11720263 | C2 | semidirect |
| 21. #88425 | C4 | semidirect |
| 48. C9×Dic6 | C2×C4 | semidirect |
| 50. C3⋊(C9⋊C8) | C2×C4 | semidirect |
| 96. C4×Dic6 | D9 | semidirect |
| 205. C3×C9 | #440 | semidirect |
| 232. Dic6 | C4×D9 | semidirect |
| 291. C9 | #5018 | semidirect |
| 329. C3 | #10588709 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×D36 | 2 |
| C4×C9×Dic6 | 2 |
| C2×#88425 | 2 |
| #11720516 | 2 |
| #11720297 | 2 |
| #11720266 | 2 |
| #11720263 | 2 |
| #10590358 | 3 |
| #10588709 | 3 |