Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
374 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 88 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×Q8×H(3,𝔽3) | C2 | semidirect |
| 3. #88549 | C2 | direct (N × H) |
| 4. C2×#6180 | C2 | semidirect |
| 8. Q8×H(3,𝔽3) | C22 | semidirect |
| 13. #6180 | C22 | semidirect |
| 14. C2×C32×Q8 | D3 | semidirect |
| 28. C32×Q8 | C2×D3 | semidirect |
| 34. C2×H(3,𝔽3) | SD16 | semidirect |
| 52. H(3,𝔽3) | C2×SD16 | semidirect |
| 69. C2×C32 | #215 | semidirect |
| 72. C2×Q8 | #272 | semidirect |
| 88. C32 | C2×#215 | semidirect |
| 91. Q8 | C2×#272 | semidirect |
| 112. C2 | #88549 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×H(3,𝔽3) | 2 |
| C2×C4⋊#272 | 2 |
| #88549 | 2 |
| C2×#6180 | 2 |
| C2×C3×#215 | 3 |