Finite Group DatabasebetaFinite Group Databasebeta← C2×((C3⋊D3)⋊C3)⋊C16 #13138717
Order 1728.
371 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 371 conjugacy classes of subgroups — too many to draw. Only its 123 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×#88386 | C2 | semidirect |
| 3. C2×(C3⋊(C3⋊C16))⋊C3 | C2 | semidirect |
| 4. ((C3⋊D3)⋊C3)⋊C16 | C2 | direct (N × H) |
| 12. #88386 | C22 | semidirect |
| 13. (C3⋊(C3⋊C16))⋊C3 | C22 | semidirect |
| 16. C2×C3⋊(C3⋊C16) | D3 | semidirect |
| 45. C3⋊(C3⋊C16) | C2×D3 | semidirect |
| 51. C2×(C3⋊D3)⋊C3 | C16 | semidirect |
| 89. C2×H(3,𝔽3) | C2×C16 | semidirect |
| 91. (C3⋊D3)⋊C3 | C2×C16 | semidirect |
| 118. C2×C3⋊D3 | C3⋊C16 | semidirect |
| 134. H(3,𝔽3) | C22×C16 | semidirect |
| 164. C2×C32 | D3×C16 | semidirect |
| 165. C2×C32 | C2×C3⋊C16 | semidirect |
| 168. C3⋊D3 | C2×C3⋊C16 | semidirect |
| 199. C32 | C2×D3×C16 | semidirect |
| 200. C32 | C22×C3⋊C16 | semidirect |
| 231. C2 | ((C3⋊D3)⋊C3)⋊C16 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×(C3⋊D3)⋊C3 | 2 |
| C2×#88386 | 2 |
| C2×(C3⋊(C3⋊C16))⋊C3 | 2 |
| ((C3⋊D3)⋊C3)⋊C16 | 2 |
| C2×#63542 | 3 |
| C2×D3×C3⋊C16 | 3 |