Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
363 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 363 conjugacy classes of subgroups — too many to draw. Only its 101 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. #11720551 | C2 | semidirect |
| 3. C2×#88386 | C2 | semidirect |
| 7. D8×H(3,𝔽3) | C4 | semidirect |
| 25. C32×D8 | Dic3 | semidirect |
| 76. H(3,𝔽3) | #357 | semidirect |
| 97. D8 | #1084 | semidirect |
| 115. C32 | #4562 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×H(3,𝔽3) | 2 |
| #11720551 | 2 |
| C2×#88386 | 2 |
| C3×#4562 | 3 |