Finite Group DatabasebetaFinite Group Databasebeta← Q8×C4⋊(C3⋊(C3⋊D3)) #13179700
Order 1728.
3920 conjugacy classes of subgroups; only the 955 normal subgroups are shown.
This group has 3920 conjugacy classes of subgroups — too many to draw. Only its 955 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×Q8×C3⋊(C3⋊D3) | C2 | semidirect |
| 2. C33×C4×Q8 | C2 | semidirect |
| 3. #11723938 | C2 | semidirect |
| 5. #11723910 | C2 | semidirect |
| 18. C32×C4×Q8 | D3 | semidirect |
| 23. C33×Q8 | D4 | semidirect |
| 28. C4⋊(C3⋊(C3⋊D3)) | Q8 | direct (N × H) |
| 45. C2×C3⋊(C3⋊D3) | C2×Q8 | semidirect |
| 48. C33×C4 | C2×Q8 | semidirect |
| 51. C3×C4×Q8 | C3⋊D3 | semidirect |
| 56. C32×Q8 | D12 | semidirect |
| 85. C32×C4 | D3×Q8 | semidirect |
| 90. C4×Q8 | C3⋊(C3⋊D3) | semidirect |
| 92. C33 | D4×Q8 | semidirect |
| 94. C3×Q8 | C4⋊(C3⋊D3) | semidirect |
| 122. C3×C4 | Q8×C3⋊D3 | semidirect |
| 124. C32 | Q8×D12 | semidirect |
| 127. Q8 | C4⋊(C3⋊(C3⋊D3)) | direct (N × H) |
| 145. C4 | Q8×C3⋊(C3⋊D3) | semidirect |
| 146. C3 | Q8×C4⋊(C3⋊D3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×C3⋊(C3⋊D3) | 2 |
| C33×C4×Q8 | 2 |
| #11723938 | 2 |
| C4×C4⋊(C3⋊(C3⋊D3)) | 2 |
| #11723910 | 2 |
| Q8×C4⋊(C3⋊D3) | 3 |