Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
495 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 495 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×Q16×H(3,𝔽3) | C2 | semidirect |
| 3. #11720569 | C2 | direct (N × H) |
| 4. C2×#88386 | C2 | semidirect |
| 9. Q16×H(3,𝔽3) | C22 | semidirect |
| 13. #88386 | C22 | semidirect |
| 14. C2×C32×Q16 | D3 | semidirect |
| 32. C32×Q16 | C2×D3 | semidirect |
| 61. C2×H(3,𝔽3) | SD32 | semidirect |
| 86. C2×Q16 | #272 | semidirect |
| 90. H(3,𝔽3) | C2×SD32 | semidirect |
| 109. C2×C32 | #828 | semidirect |
| 115. Q16 | C2×#272 | semidirect |
| 132. C32 | C2×#828 | semidirect |
| 157. C2 | #11720569 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×H(3,𝔽3) | 2 |
| C2×#88529 | 2 |
| #11720569 | 2 |
| C2×#88386 | 2 |
| C2×C3×#828 | 3 |