Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
715 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 715 conjugacy classes of subgroups — too many to draw. Only its 92 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. C23×#272 | C2 | semidirect |
| 2. C2×D4×H(3,𝔽3) | C2 | semidirect |
| 3. C2×#6235 | C2 | semidirect |
| 4. #88552 | C2 | semidirect |
| 5. #88542 | C2 | semidirect |
| 8. C23×H(3,𝔽3) | C22 | semidirect |
| 13. C2×C4×H(3,𝔽3) | C22 | semidirect |
| 15. C2×#1084 | C22 | semidirect |
| 17. C2×C32×D4 | D3 | semidirect |
| 24. C22×H(3,𝔽3) | D4 | semidirect |
| 29. C2×#272 | D4 | semidirect |
| 35. C23×C32 | C2×D3 | semidirect |
| 40. C2×C32×C4 | C2×D3 | semidirect |
| 61. C22×C32 | #67 | semidirect |
| 70. H(3,𝔽3) | #120 | semidirect |
| 96. C2×D4 | #272 | semidirect |
| 121. C32 | #937 | semidirect |
| 126. C23 | C2×#272 | semidirect |
| 130. C2×C4 | C2×#272 | semidirect |
| 148. C22 | #6235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#272 | 2 |
| C2×D4×H(3,𝔽3) | 2 |
| C2×#6235 | 2 |
| #88552 | 2 |
| #88542 | 2 |
| C3×#937 | 3 |