Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1124 conjugacy classes of subgroups; only the 236 normal subgroups are shown.
This group has 1124 conjugacy classes of subgroups — too many to draw. Only its 236 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. #11723910 | C2 | semidirect |
| 3. C2×#88796 | C2 | semidirect |
| 4. C32×C4×C3⋊C8 | C2 | semidirect |
| 22. C3×C4×C3⋊C8 | D3 | semidirect |
| 30. C32×C3⋊C8 | D4 | semidirect |
| 53. C33×C4 | SD16 | semidirect |
| 64. C4×C3⋊C8 | C3⋊D3 | semidirect |
| 84. C3×C3⋊C8 | D12 | semidirect |
| 115. C32×C4 | #204 | semidirect |
| 116. C32×C4 | #214 | semidirect |
| 126. C33 | #492 | semidirect |
| 146. C3⋊C8 | C4⋊(C3⋊D3) | semidirect |
| 171. C3×C4 | #3716 | semidirect |
| 172. C3×C4 | #3744 | semidirect |
| 179. C32 | #4693 | semidirect |
| 180. C32 | #5076 | semidirect |
| 201. C4 | #88796 | semidirect |
| 204. C3 | #10590369 | semidirect |
| 205. C3 | #10592392 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723910 | 2 |
| C3×#64083 | 2 |
| C2×#88796 | 2 |
| C32×C4×C3⋊C8 | 2 |
| #10592392 | 3 |
| #10590369 | 3 |