Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1979 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1979 conjugacy classes of subgroups — too many to draw. Only its 251 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. C22×C4⋊#272 | C2 | semidirect |
| 2. C22×C4⋊((C3⋊D3)⋊C3) | C2 | semidirect |
| 3. C22×#6200 | C2 | semidirect |
| 4. C2×C4×(C3⋊Dic3)⋊C3 | C2 | semidirect |
| 5. #11721158 | C2 | direct (N × H) |
| 12. C2×C4⋊#272 | C22 | semidirect |
| 15. C2×C4⋊((C3⋊D3)⋊C3) | C22 | semidirect |
| 17. C2×#6200 | C22 | semidirect |
| 18. C4×(C3⋊Dic3)⋊C3 | C22 | semidirect |
| 19. C22×C4⋊(C3⋊D3) | D3 | semidirect |
| 26. C2×C4×C3⋊Dic3 | D3 | semidirect |
| 37. C2×C4×H(3,𝔽3) | D4 | semidirect |
| 40. C2×(C3⋊Dic3)⋊C3 | D4 | semidirect |
| 57. C2×C4⋊(C3⋊D3) | C2×D3 | semidirect |
| 71. C4×C3⋊Dic3 | C2×D3 | semidirect |
| 82. C4×H(3,𝔽3) | C2×D4 | semidirect |
| 83. (C3⋊Dic3)⋊C3 | C2×D4 | semidirect |
| 120. C2×C32×C4 | D12 | semidirect |
| 121. C2×C32×C4 | #67 | semidirect |
| 124. C2×C3⋊Dic3 | D12 | semidirect |
| 136. C2×H(3,𝔽3) | #127 | semidirect |
| 203. C32×C4 | C2×D12 | semidirect |
| 204. C32×C4 | C2×#67 | semidirect |
| 205. C3⋊Dic3 | C2×D12 | semidirect |
| 212. H(3,𝔽3) | C2×#127 | semidirect |
| 265. C2×C32 | #874 | semidirect |
| 266. C2×C32 | #940 | semidirect |
| 328. C32 | C2×#874 | semidirect |
| 329. C32 | C2×#940 | semidirect |
| 342. C2×C4 | #6200 | semidirect |
| 373. C4 | C2×#6200 | semidirect |
| 380. C2 | #11721158 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#272 | 2 |
| C22×C4⋊((C3⋊D3)⋊C3) | 2 |
| C22×#6200 | 2 |
| C2×C4×(C3⋊Dic3)⋊C3 | 2 |
| #11721158 | 2 |
| C2×#63914 | 3 |
| C2×#63911 | 3 |