Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
374 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 74 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. #88740 | C2 | semidirect |
| 3. #88546 | C2 | semidirect |
| 4. #88545 | C2 | semidirect |
| 5. #88538 | C2 | semidirect |
| 13. C4⋊#272 | C22 | semidirect |
| 15. #6229 | C22 | semidirect |
| 16. #6180 | C22 | semidirect |
| 17. C2×C32×D4 | D3 | semidirect |
| 18. C2×C32×D4 | D3 | semidirect |
| 89. H(3,𝔽3) | AGL(1,ℤ/8) | semidirect |
| 126. C2×D4 | #272 | semidirect |
| 151. C32 | #932 | semidirect |
| 152. C32 | #932 | 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 |
| #88740 | 2 |
| #88546 | 2 |
| #88545 | 2 |
| #88538 | 2 |
| C3×#932 | 3 |