Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
757 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 757 conjugacy classes of subgroups — too many to draw. Only its 111 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. C2×C8×(C3⋊D3)⋊C3 | C2 | semidirect |
| 3. #11721129 | C2 | semidirect |
| 4. #11720554 | C2 | semidirect |
| 5. #63648⋊C3 | C2 | semidirect |
| 6. #11720324 | C2 | semidirect |
| 7. #11720308 | C2 | semidirect |
| 17. #88654 | C4 | semidirect |
| 18. C2×C8×H(3,𝔽3) | C22 | semidirect |
| 19. C4⋊#1084 | C22 | semidirect |
| 20. C4⋊((C3⋊Dic3)⋊C3) | C22 | semidirect |
| 21. C2×(C3⋊(C3⋊C8))⋊C3 | C22 | semidirect |
| 26. C2×C8×C3⋊D3 | D3 | semidirect |
| 30. #63648 | D3 | semidirect |
| 48. C4⋊#272 | C2×C4 | semidirect |
| 52. C4⋊((C3⋊D3)⋊C3) | C2×C4 | semidirect |
| 80. C2×C32×C8 | C2×D3 | semidirect |
| 81. C2×C32×C8 | C2×D3 | semidirect |
| 82. C4⋊(C3⋊Dic3) | C2×D3 | semidirect |
| 83. C2×C3⋊(C3⋊C8) | C2×D3 | semidirect |
| 150. C4⋊(C3⋊D3) | C4×D3 | semidirect |
| 183. (C3⋊D3)⋊C3 | #102 | semidirect |
| 275. H(3,𝔽3) | C2×#102 | semidirect |
| 352. C3⋊D3 | #821 | semidirect |
| 368. C2×C8 | ((C3⋊D3)⋊C3)⋊C2 | semidirect |
| 428. C32 | D3×#102 | semidirect |
| 429. C32 | C2×#821 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88654 | 2 |
| C2×C8×(C3⋊D3)⋊C3 | 2 |
| #11721129 | 2 |
| #11720554 | 2 |
| #63648⋊C3 | 2 |
| #11720324 | 2 |
| #11720308 | 2 |
| #10590940 | 3 |
| D3×#821 | 3 |