Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1876 conjugacy classes of subgroups; only the 523 normal subgroups are shown.
This group has 1876 conjugacy classes of subgroups — too many to draw. Only its 523 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. C33×C4×D4 | C2 | semidirect |
| 3. C4×C4⋊(C3⋊(C3⋊D3)) | C2 | semidirect |
| 4. #11722202 | C2 | semidirect |
| 5. #11722179 | C2 | semidirect |
| 6. #11722177 | C2 | semidirect |
| 7. C4×C3⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 16. #88860 | C4 | direct (N × H) |
| 21. C32×C4×D4 | D3 | semidirect |
| 31. C33×D4 | C2×C4 | semidirect |
| 39. C4⋊(C3⋊(C3⋊D3)) | C2×C4 | semidirect |
| 42. C3⋊(C3⋊(C3⋊C8)) | C2×C4 | semidirect |
| 65. C33×C4 | D8 | semidirect |
| 69. C3×C4×D4 | C3⋊D3 | semidirect |
| 79. C32×D4 | C4×D3 | semidirect |
| 118. C32×C4 | #213 | semidirect |
| 124. C4×D4 | C3⋊(C3⋊D3) | semidirect |
| 129. C33 | C4×D8 | semidirect |
| 133. C3×D4 | C4×C3⋊D3 | semidirect |
| 171. C3×C4 | #3753 | semidirect |
| 175. C32 | C4×#213 | semidirect |
| 181. D4 | C4×C3⋊(C3⋊D3) | semidirect |
| 206. C4 | #88860 | direct (N × H) |
| 209. C3 | C4×#3753 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C4×D4 | 2 |
| C2×#88860 | 2 |
| C4×C4⋊(C3⋊(C3⋊D3)) | 2 |
| #11722202 | 2 |
| #11722179 | 2 |
| #11722177 | 2 |
| C4×C3⋊(C3⋊(C3⋊C8)) | 2 |
| C4×#3753 | 3 |