Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
902 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 902 conjugacy classes of subgroups — too many to draw. Only its 172 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. #41×H(3,𝔽3) | C2 | semidirect |
| 2. #88748 | C2 | semidirect |
| 3. Q8×#272 | C2 | semidirect |
| 4. #88744 | C2 | semidirect |
| 5. D4×#272 | C2 | semidirect |
| 6. #88740 | C2 | semidirect |
| 7. C2×C4×#272 | C2 | semidirect |
| 11. Q8×H(3,𝔽3) | C22 | semidirect |
| 12. D4×H(3,𝔽3) | C22 | semidirect |
| 13. C2×C4×H(3,𝔽3) | C22 | semidirect |
| 14. #6235 | C22 | semidirect |
| 15. C2×#1084 | C22 | semidirect |
| 16. C4⋊#272 | C22 | semidirect |
| 19. C4×#272 | C22 | semidirect |
| 20. C4×#272 | C22 | semidirect |
| 21. #6229 | C22 | semidirect |
| 22. C32×#41 | D3 | semidirect |
| 23. C32×#41 | D3 | semidirect |
| 49. C32×Q8 | C2×D3 | semidirect |
| 50. C32×Q8 | C2×D3 | semidirect |
| 51. C32×D4 | C2×D3 | semidirect |
| 52. C32×D4 | C2×D3 | semidirect |
| 53. C2×C32×C4 | C2×D3 | semidirect |
| 54. C2×C32×C4 | C2×D3 | semidirect |
| 74. #272 | #41 | direct (N × H) |
| 113. H(3,𝔽3) | C2×#41 | semidirect |
| 161. #41 | #272 | direct (N × H) |
| 189. C32 | D3×#41 | semidirect |
| 190. C32 | D3×#41 | semidirect |
| 193. Q8 | C2×#272 | semidirect |
| 196. D4 | C2×#272 | semidirect |
| 202. C2×C4 | C2×#272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×H(3,𝔽3) | 2 |
| #88748 | 2 |
| Q8×#272 | 2 |
| #88744 | 2 |
| D4×#272 | 2 |
| #88740 | 2 |
| C2×C4×#272 | 2 |
| C3×D3×#41 | 3 |