Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
430 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 430 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 |
|---|---|---|
| 1. C4×#6226 | C2 | semidirect |
| 4. C9×#803 | C2 | semidirect |
| 6. #11720279 | C2 | semidirect |
| 7. #11720277 | C2 | semidirect |
| 21. #88415 | C4 | semidirect |
| 44. #6226 | C2×C4 | semidirect |
| 50. C9×C3⋊C8 | C2×C4 | semidirect |
| 107. #803 | D9 | semidirect |
| 213. C3×C9 | #440 | semidirect |
| 248. C3⋊C8 | C4×D9 | semidirect |
| 303. C9 | #5018 | semidirect |
| 341. C3 | #10588391 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#6226 | 2 |
| C3×C4×D36 | 2 |
| C2×#88415 | 2 |
| C9×#803 | 2 |
| #11720283 | 2 |
| #11720279 | 2 |
| #11720277 | 2 |
| #10590360 | 3 |
| #10588391 | 3 |