Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
628 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 628 conjugacy classes of subgroups — too many to draw. Only its 124 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×C4⋊#272 | C2 | semidirect |
| 2. C2×C4×(C3⋊D3)⋊C3 | C2 | semidirect |
| 3. C2×#634⋊C3 | C2 | semidirect |
| 4. C2×#6200 | C2 | semidirect |
| 5. C2×#6199 | C2 | semidirect |
| 6. #88652 | C2 | direct (N × H) |
| 12. C4⋊#272 | C22 | semidirect |
| 15. C4×(C3⋊D3)⋊C3 | C22 | semidirect |
| 16. #634⋊C3 | C22 | semidirect |
| 17. #6200 | C22 | semidirect |
| 18. #6199 | C22 | semidirect |
| 19. C2×C4×C3⋊D3 | D3 | semidirect |
| 20. C2×#634 | D3 | semidirect |
| 53. C4×C3⋊D3 | C2×D3 | semidirect |
| 54. #634 | C2×D3 | semidirect |
| 66. C2×H(3,𝔽3) | #41 | semidirect |
| 110. H(3,𝔽3) | C2×#41 | semidirect |
| 146. C2×C32 | #235 | semidirect |
| 147. C2×C32 | #239 | semidirect |
| 190. C32 | C2×#235 | semidirect |
| 191. C32 | C2×#239 | semidirect |
| 231. C2 | #88652 | 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×C4×(C3⋊D3)⋊C3 | 2 |
| C2×#634⋊C3 | 2 |
| C2×#6200 | 2 |
| C2×#6199 | 2 |
| #88652 | 2 |
| C2×#3796 | 3 |
| C2×#3795 | 3 |