Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
598 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 598 conjugacy classes of subgroups — too many to draw. Only its 89 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. #11721720 | C2 | semidirect |
| 2. C4×C4⋊((C3⋊D3)⋊C3) | C2 | semidirect |
| 3. C2×#88436 | C2 | semidirect |
| 4. C4⋊((C3⋊(C3⋊C8))⋊C3) | C2 | semidirect |
| 5. #11720324 | C2 | semidirect |
| 18. C4×C4⋊(C3⋊D3) | D3 | semidirect |
| 25. C4⋊(C3⋊(C3⋊C8)) | D3 | semidirect |
| 40. C4⋊((C3⋊D3)⋊C3) | D4 | semidirect |
| 78. C4×H(3,𝔽3) | D8 | semidirect |
| 114. C4⋊(C3⋊D3) | D12 | semidirect |
| 198. C32×C4 | D24 | semidirect |
| 199. C32×C4 | #213 | semidirect |
| 211. H(3,𝔽3) | #459 | semidirect |
| 331. C32 | #4843 | semidirect |
| 332. C32 | #5015 | semidirect |
| 375. C4 | #88436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721720 | 2 |
| C4×C4⋊((C3⋊D3)⋊C3) | 2 |
| C2×#88436 | 2 |
| C4⋊((C3⋊(C3⋊C8))⋊C3) | 2 |
| #11720324 | 2 |
| #10590355 | 3 |
| #10590347 | 3 |