Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
374 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 2. C2×C8×H(3,𝔽3) | C2 | semidirect |
| 3. C2×#6180 | C2 | semidirect |
| 4. #88527 | C2 | direct (N × H) |
| 11. C8×H(3,𝔽3) | C22 | semidirect |
| 12. #6180 | C22 | semidirect |
| 14. C2×C32×C8 | D3 | semidirect |
| 30. C32×C8 | C2×D3 | semidirect |
| 32. C2×H(3,𝔽3) | M16 | semidirect |
| 50. H(3,𝔽3) | C2×M16 | semidirect |
| 65. C2×C32 | ΓL(1,𝔽25) | semidirect |
| 71. C2×C8 | #272 | semidirect |
| 84. C32 | C2×ΓL(1,𝔽25) | semidirect |
| 91. C8 | C2×#272 | semidirect |
| 107. C2 | #88527 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#272 | 2 |
| C2×C8×H(3,𝔽3) | 2 |
| C2×#6180 | 2 |
| #88527 | 2 |
| C2×C3×ΓL(1,𝔽25) | 3 |