Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
4340 conjugacy classes of subgroups; only the 1003 normal subgroups are shown.
This group has 4340 conjugacy classes of subgroups — too many to draw. Only its 1003 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×#89076 | C2 | semidirect |
| 2. C2×C33×C42 | C2 | semidirect |
| 3. #11723971 | C2 | semidirect |
| 4. #11723916 | C2 | semidirect |
| 5. #11723915 | C2 | semidirect |
| 6. C4×C4⋊(C3⋊(C3⋊D3)) | C2 | semidirect |
| 7. #11723910 | C2 | semidirect |
| 23. C2×C32×C42 | D3 | semidirect |
| 32. C2×C33×C4 | D4 | semidirect |
| 65. C33×C4 | #41 | semidirect |
| 68. C2×C3×C42 | C3⋊D3 | semidirect |
| 77. C2×C32×C4 | D12 | semidirect |
| 114. C32×C4 | #235 | semidirect |
| 122. C2×C42 | C3⋊(C3⋊D3) | semidirect |
| 123. C33 | #532 | semidirect |
| 127. C2×C3×C4 | C4⋊(C3⋊D3) | semidirect |
| 163. C3×C4 | #3828 | semidirect |
| 165. C32 | #5477 | semidirect |
| 175. C2×C4 | C4⋊(C3⋊(C3⋊D3)) | semidirect |
| 193. C4 | #89076 | semidirect |
| 194. C3 | #10595948 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89076 | 2 |
| C2×C33×C42 | 2 |
| #11723971 | 2 |
| #11723916 | 2 |
| #11723915 | 2 |
| C4×C4⋊(C3⋊(C3⋊D3)) | 2 |
| #11723910 | 2 |
| #10595948 | 3 |