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. #88740 | C2 | semidirect |
| 2. C2×C4⋊#272 | C2 | semidirect |
| 3. M16×H(3,𝔽3) | C2 | semidirect |
| 4. #88529 | C2 | semidirect |
| 5. #88528 | C2 | semidirect |
| 12. C4⋊#272 | C22 | semidirect |
| 14. #6229 | C22 | semidirect |
| 15. C8×H(3,𝔽3) | C22 | semidirect |
| 18. C32×M16 | D3 | semidirect |
| 38. C32×C8 | C2×D3 | semidirect |
| 61. H(3,𝔽3) | AGL(1,ℤ/8) | semidirect |
| 88. M16 | #272 | semidirect |
| 103. C32 | #908 | semidirect |
| 112. C8 | C2×#272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #88740 | 2 |
| C2×C4⋊#272 | 2 |
| M16×H(3,𝔽3) | 2 |
| #88529 | 2 |
| #88528 | 2 |
| C3×#908 | 3 |