Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
591 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 591 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 3. C4⋊((C3⋊(C3⋊C8))⋊C3) | C2 | semidirect |
| 4. #11720304 | C2 | semidirect |
| 18. C4⋊(C3⋊(C3⋊C8)) | D3 | semidirect |
| 29. C4×#272 | C8 | semidirect |
| 57. C4×H(3,𝔽3) | C2×C8 | semidirect |
| 62. #1084 | C2×C8 | semidirect |
| 101. #272 | C4⋊C8 | semidirect |
| 141. C32×C4 | D3×C8 | semidirect |
| 154. H(3,𝔽3) | C2×C4⋊C8 | semidirect |
| 242. C32 | D3×C4⋊C8 | semidirect |
| 275. C4 | #88434 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×#272 | 2 |
| C2×#88434 | 2 |
| C4⋊((C3⋊(C3⋊C8))⋊C3) | 2 |
| #11720304 | 2 |
| D3×C4⋊(C3⋊C8) | 3 |