Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
482 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 112 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. #11724364 | C2 | semidirect |
| 2. #11724362 | C2 | semidirect |
| 3. #11724361 | C2 | semidirect |
| 4. C3×C4⋊PSU(3,𝔽2) | C2 | semidirect |
| 8. #11724153 | C2 | semidirect |
| 9. #11724152 | C2 | semidirect |
| 43. C4⋊PSU(3,𝔽2) | D3 | semidirect |
| 59. C4×C3⋊(C3⋊D3) | Q8 | semidirect |
| 61. C32×C4×D3 | Q8 | semidirect |
| 62. #6289 | Q8 | semidirect |
| 64. D3×C3⋊Dic3 | Q8 | semidirect |
| 214. C33 | #544 | semidirect |
| 239. C4×D3 | PSU(3,𝔽2) | semidirect |
| 307. C32 | #5729 | semidirect |
| 357. C3 | #10596543 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724364 | 2 |
| #11724362 | 2 |
| #11724361 | 2 |
| C3×C4⋊PSU(3,𝔽2) | 2 |
| D3×C4⋊#157 | 2 |
| #11724247 | 2 |
| #11724246 | 2 |
| #11724153 | 2 |
| #11724152 | 2 |
| #11724151 | 2 |
| #11724149 | 2 |
| #10596543 | 3 |
| #5729 | 9 |