Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
517 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 517 conjugacy classes of subgroups — too many to draw. Only its 90 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. C2×D4×H(3,𝔽3) | C2 | semidirect |
| 2. C2×#6235 | C2 | semidirect |
| 3. C2×#6235 | C2 | semidirect |
| 4. C22×#1084 | C2 | semidirect |
| 5. #88552 | C2 | semidirect |
| 6. #88542 | C2 | semidirect |
| 7. #88540 | C2 | semidirect |
| 20. C2×C32×D4 | D3 | semidirect |
| 32. C22×H(3,𝔽3) | D4 | semidirect |
| 40. #1084 | D4 | semidirect |
| 79. C22×C32 | #67 | semidirect |
| 89. H(3,𝔽3) | #121 | semidirect |
| 120. C2×D4 | #272 | semidirect |
| 153. C32 | #939 | semidirect |
| 185. C22 | #6235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×H(3,𝔽3) | 2 |
| C2×#6235 | 2 |
| C22×#1084 | 2 |
| #88552 | 2 |
| #88542 | 2 |
| #88540 | 2 |
| C3×#939 | 3 |