Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
514 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 118 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. C4×C3⋊PSU(3,𝔽2) | C2 | semidirect |
| 2. C4×C3⋊PSU(3,𝔽2) | C2 | semidirect |
| 3. C3×C4×PSU(3,𝔽2) | C2 | semidirect |
| 6. #11724154 | C2 | semidirect |
| 7. #11724153 | C2 | semidirect |
| 8. #11724152 | C2 | semidirect |
| 45. C4×PSU(3,𝔽2) | D3 | semidirect |
| 61. C4×C3⋊(C3⋊D3) | Q8 | semidirect |
| 63. C32×C4×D3 | Q8 | semidirect |
| 64. #6289 | Q8 | semidirect |
| 66. D3×C3⋊Dic3 | Q8 | semidirect |
| 218. C33 | #533 | semidirect |
| 244. C4×D3 | PSU(3,𝔽2) | semidirect |
| 313. C32 | #5578 | semidirect |
| 365. C3 | #10596542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C3⋊PSU(3,𝔽2) | 2 |
| C3×C4×PSU(3,𝔽2) | 2 |
| C4×D3×#157 | 2 |
| #11724246 | 2 |
| #11724154 | 2 |
| #11724153 | 2 |
| #11724152 | 2 |
| #11724151 | 2 |
| #11724150 | 2 |
| #11724149 | 2 |
| #10596542 | 3 |
| #5578 | 9 |