Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
546 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 123 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. C3×D4×H(3,𝔽3) | C2 | semidirect |
| 2. C4⋊(C3⋊#272) | C2 | semidirect |
| 3. C3⋊#6180 | C2 | semidirect |
| 9. C33×D4 | D3 | semidirect |
| 12. D4×H(3,𝔽3) | D3 | semidirect |
| 27. C3×H(3,𝔽3) | D8 | semidirect |
| 31. C32×D4 | C3⋊D3 | semidirect |
| 58. C33 | #213 | semidirect |
| 59. H(3,𝔽3) | #213 | semidirect |
| 63. C3×D4 | #272 | semidirect |
| 96. C32 | #3753 | semidirect |
| 98. D4 | C3⋊#272 | semidirect |
| 116. C3 | #88545 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×D4×H(3,𝔽3) | 2 |
| C4⋊(C3⋊#272) | 2 |
| C3⋊#6180 | 2 |
| C3×#3753 | 3 |
| #88545 | 3 |