Finite Group DatabasebetaFinite Group Databasebeta← D4×C3⋊(C3⋊(C3⋊C8)) #13163650
Order 1728.
1876 conjugacy classes of subgroups; only the 909 normal subgroups are shown.
This group has 1876 conjugacy classes of subgroups — too many to draw. Only its 909 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 |
|---|---|---|
| 2. C22×C3⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 3. #11722200 | C2 | semidirect |
| 4. C4⋊(C3⋊(C3⋊(C3⋊C8))) | C2 | semidirect |
| 5. C4×C3⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 22. C33×D4 | C8 | semidirect |
| 31. C3⋊(C3⋊(C3⋊C8)) | D4 | direct (N × H) |
| 44. C22×C33 | C2×C8 | semidirect |
| 48. C33×C4 | C2×C8 | semidirect |
| 57. C32×D4 | C3⋊C8 | semidirect |
| 83. C22×C32 | C2×C3⋊C8 | semidirect |
| 87. C32×C4 | C2×C3⋊C8 | semidirect |
| 95. C33 | C8×D4 | semidirect |
| 97. C3×D4 | C3⋊(C3⋊C8) | semidirect |
| 122. C22×C3 | C2×C3⋊(C3⋊C8) | semidirect |
| 126. C3×C4 | C2×C3⋊(C3⋊C8) | semidirect |
| 129. C32 | D4×C3⋊C8 | semidirect |
| 131. D4 | C3⋊(C3⋊(C3⋊C8)) | direct (N × H) |
| 147. C22 | C2×C3⋊(C3⋊(C3⋊C8)) | semidirect |
| 151. C4 | C2×C3⋊(C3⋊(C3⋊C8)) | semidirect |
| 154. C3 | D4×C3⋊(C3⋊C8) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C4×D4 | 2 |
| C22×C3⋊(C3⋊(C3⋊C8)) | 2 |
| #11722200 | 2 |
| C4⋊(C3⋊(C3⋊(C3⋊C8))) | 2 |
| C4×C3⋊(C3⋊(C3⋊C8)) | 2 |
| D4×C3⋊(C3⋊C8) | 3 |