Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
517 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 517 conjugacy classes of subgroups — too many to draw. Only its 102 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×H(3,𝔽3) | C2 | semidirect |
| 2. C2×#6235 | C2 | semidirect |
| 3. C2×C4⋊#272 | C2 | semidirect |
| 4. #88542 | C2 | semidirect |
| 5. C4⋊#1084 | C2 | semidirect |
| 15. C22×C32×C4 | D3 | semidirect |
| 22. C22×H(3,𝔽3) | D4 | semidirect |
| 28. C4×H(3,𝔽3) | D4 | semidirect |
| 57. C22×C32 | D12 | semidirect |
| 63. C32×C4 | #67 | semidirect |
| 66. H(3,𝔽3) | #121 | semidirect |
| 90. C22×C4 | #272 | semidirect |
| 113. C32 | #930 | semidirect |
| 137. C22 | C4⋊#272 | semidirect |
| 141. C4 | #6235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×H(3,𝔽3) | 2 |
| C2×#6235 | 2 |
| C2×C4⋊#272 | 2 |
| #88542 | 2 |
| C4⋊#1084 | 2 |
| C3×#930 | 3 |