Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
990 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 990 conjugacy classes of subgroups — too many to draw. Only its 175 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. C22×C4⋊(C3⋊D9) | C2 | semidirect |
| 2. C3×C9×#121 | C2 | semidirect |
| 3. C2×#88544 | C2 | semidirect |
| 4. #11720571 | C2 | semidirect |
| 5. #11720528 | C2 | semidirect |
| 10. C2×C3×D4×C9 | C22 | semidirect |
| 15. C3×C9×C4⋊C4 | C22 | semidirect |
| 18. C2×C3⋊(C9⋊C8) | C22 | semidirect |
| 25. C9×#121 | D3 | semidirect |
| 43. C4⋊(C3⋊D9) | D4 | semidirect |
| 60. C2×D4×C9 | C2×D3 | semidirect |
| 65. C9×C4⋊C4 | C2×D3 | semidirect |
| 74. C22×C3×C9 | D8 | semidirect |
| 85. C3×#121 | D9 | semidirect |
| 136. C2×C3×D4 | C2×D9 | semidirect |
| 146. C3×C4⋊C4 | C2×D9 | semidirect |
| 173. C22×C9 | #213 | semidirect |
| 184. #121 | C3⋊D9 | semidirect |
| 187. C3×C9 | #447 | semidirect |
| 237. C2×D4 | C2×C3⋊D9 | semidirect |
| 241. C4⋊C4 | C2×C3⋊D9 | semidirect |
| 253. C22×C3 | #3673 | semidirect |
| 272. C9 | #5036 | semidirect |
| 310. C22 | #88544 | semidirect |
| 315. C3 | #10588719 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊(C3⋊D9) | 2 |
| C3×C9×#121 | 2 |
| C2×#88544 | 2 |
| #11720571 | 2 |
| #11720528 | 2 |
| #10592735 | 3 |
| #10588719 | 3 |