Finite Group DatabasebetaFinite Group Databasebeta← Q8×((C3⋊D3)⋊C3)⋊C2 #11722518
Order 864.
584 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 128 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. Q8×#272 | C2 | semidirect |
| 2. Q8×(C3⋊D3)⋊C3 | C2 | semidirect |
| 4. #88651 | C2 | semidirect |
| 5. ((C3⋊D3)⋊C3)⋊Q8 | C2 | semidirect |
| 8. Q8×H(3,𝔽3) | C22 | semidirect |
| 10. #6229 | C22 | semidirect |
| 12. #634⋊C3 | C22 | semidirect |
| 15. #6196 | C22 | semidirect |
| 16. Q8×C3⋊D3 | D3 | semidirect |
| 26. ((C3⋊D3)⋊C3)⋊C2 | Q8 | direct (N × H) |
| 34. C32×Q8 | C2×D3 | semidirect |
| 36. #634 | C2×D3 | semidirect |
| 48. #272 | C2×Q8 | semidirect |
| 49. (C3⋊D3)⋊C3 | C2×Q8 | semidirect |
| 75. H(3,𝔽3) | C22×Q8 | semidirect |
| 102. C3⋊D3 | D3×Q8 | semidirect |
| 129. C32 | C2×D3×Q8 | semidirect |
| 134. Q8 | ((C3⋊D3)⋊C3)⋊C2 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#272 | 2 |
| Q8×(C3⋊D3)⋊C3 | 2 |
| C4×((C3⋊D3)⋊C3)⋊C2 | 2 |
| #88651 | 2 |
| ((C3⋊D3)⋊C3)⋊Q8 | 2 |
| D32×Q8 | 3 |