Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
528 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 117 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×C9×ΓL(1,𝔽25) | C2 | semidirect |
| 3. D3×C4⋊Dic9 | C2 | semidirect |
| 4. #11720539 | C2 | semidirect |
| 5. C3×#63380 | C2 | semidirect |
| 6. #11720283 | C2 | semidirect |
| 7. #11720277 | C2 | semidirect |
| 17. #88641 | C4 | semidirect |
| 35. #63380 | D3 | semidirect |
| 45. #6226 | C2×C4 | semidirect |
| 51. C3×D36 | C2×C4 | semidirect |
| 107. C2×ΓL(1,𝔽25) | D9 | semidirect |
| 151. D36 | C4×D3 | semidirect |
| 235. C3×C9 | #417 | semidirect |
| 338. C9 | #4771 | semidirect |
| 384. C3 | #10588815 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88641 | 2 |
| C2×C9×ΓL(1,𝔽25) | 2 |
| D3×C4⋊Dic9 | 2 |
| #11720539 | 2 |
| C3×#63380 | 2 |
| #11720283 | 2 |
| #11720277 | 2 |
| #10590670 | 3 |
| #10588815 | 3 |