Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
343 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 343 conjugacy classes of subgroups — too many to draw. Only its 107 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. #11720247 | 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 |
| 89. C2×H(3,𝔽3) | M32 | semidirect |
| 134. H(3,𝔽3) | C2×M32 | semidirect |
| 164. C2×C32 | #798 | semidirect |
| 165. C2×C32 | #812 | semidirect |
| 199. C32 | C2×#798 | semidirect |
| 200. C32 | C2×#812 | semidirect |
| 231. C2 | #11720247 | 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 |
| #11720247 | 2 |
| C2×#63544 | 3 |
| C2×#63543 | 3 |