Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
383 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 383 conjugacy classes of subgroups — too many to draw. Only its 103 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. C22×C4×H(3,𝔽3) | C2 | semidirect |
| 3. C2×C4×(C3⋊D3)⋊C3 | C2 | semidirect |
| 4. #3757⋊C3 | C2 | semidirect |
| 5. #3752⋊C3 | C2 | semidirect |
| 6. #3750⋊C3 | C2 | semidirect |
| 7. C4×(C3⋊Dic3)⋊C3 | C2 | semidirect |
| 8. C4×#638 | C3 | semidirect |
| 15. #638⋊C3 | C4 | direct (N × H) |
| 21. C22×C32×C4 | D3 | semidirect |
| 22. C22×C32×C4 | C2×C3 | semidirect |
| 24. C2×C4×C3⋊D3 | C2×C3 | semidirect |
| 27. #3757 | C2×C3 | semidirect |
| 28. #3752 | C2×C3 | semidirect |
| 29. #3750 | C2×C3 | semidirect |
| 30. C4×C3⋊Dic3 | C2×C3 | semidirect |
| 37. C22×H(3,𝔽3) | C2×C4 | semidirect |
| 41. C2×(C3⋊D3)⋊C3 | C2×C4 | semidirect |
| 43. C4×H(3,𝔽3) | D4 | semidirect |
| 46. (C3⋊Dic3)⋊C3 | C2×C4 | semidirect |
| 64. #638 | C3×C4 | semidirect |
| 109. C22×C32 | C4×D3 | semidirect |
| 110. C22×C32 | C2×C3×C4 | semidirect |
| 115. C2×C3⋊D3 | C2×C3×C4 | semidirect |
| 123. C32×C4 | #67 | semidirect |
| 124. C32×C4 | C3×D4 | semidirect |
| 127. C3⋊Dic3 | C2×C3×C4 | semidirect |
| 132. H(3,𝔽3) | C4×D4 | semidirect |
| 183. C22×C4 | (C3⋊D3)⋊C3 | semidirect |
| 231. C32 | C4×#67 | semidirect |
| 232. C32 | C3×C4×D4 | semidirect |
| 267. C22 | C4×(C3⋊D3)⋊C3 | semidirect |
| 273. C4 | #638⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×H(3,𝔽3) | 2 |
| C2×#638⋊C3 | 2 |
| C2×C4×(C3⋊D3)⋊C3 | 2 |
| #3757⋊C3 | 2 |
| #3752⋊C3 | 2 |
| #3750⋊C3 | 2 |
| C4×(C3⋊Dic3)⋊C3 | 2 |
| C4×#638 | 3 |
| C3×C4×#67 | 3 |