Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
320 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 77 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. C2×C4⋊((C3⋊D3)⋊C3) | C2 | semidirect |
| 3. #3753⋊C3 | C2 | direct (N × H) |
| 4. C2×(C3⋊(C3⋊C8))⋊C3 | C2 | semidirect |
| 5. C2×#3753 | C3 | semidirect |
| 10. D4×H(3,𝔽3) | C22 | semidirect |
| 13. C4⋊((C3⋊D3)⋊C3) | C22 | semidirect |
| 14. (C3⋊(C3⋊C8))⋊C3 | C22 | semidirect |
| 16. C2×C32×D4 | D3 | semidirect |
| 17. C2×C32×D4 | C2×C3 | semidirect |
| 18. C2×C4⋊(C3⋊D3) | C2×C3 | semidirect |
| 20. #3753 | C2×C3 | semidirect |
| 21. C2×C3⋊(C3⋊C8) | C2×C3 | semidirect |
| 43. C32×D4 | C2×D3 | semidirect |
| 44. C32×D4 | C22×C3 | semidirect |
| 49. C4⋊(C3⋊D3) | C22×C3 | semidirect |
| 52. C3⋊(C3⋊C8) | C22×C3 | semidirect |
| 55. C2×H(3,𝔽3) | D8 | semidirect |
| 91. H(3,𝔽3) | C2×D8 | semidirect |
| 125. C2×C32 | #213 | semidirect |
| 126. C2×C32 | C3×D8 | semidirect |
| 132. C2×D4 | (C3⋊D3)⋊C3 | semidirect |
| 162. C32 | C2×#213 | semidirect |
| 163. C32 | C2×C3×D8 | semidirect |
| 169. D4 | C2×(C3⋊D3)⋊C3 | semidirect |
| 200. C2 | #3753⋊C3 | direct (N × H) |
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 |
| C2×C4⋊((C3⋊D3)⋊C3) | 2 |
| #3753⋊C3 | 2 |
| C2×(C3⋊(C3⋊C8))⋊C3 | 2 |
| C2×#3753 | 3 |
| C2×C3×#213 | 3 |