Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
944 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 176 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×C32×ΓL(1,𝔽25) | C2 | semidirect |
| 3. C2×#88785 | C2 | semidirect |
| 4. #11722190 | C2 | semidirect |
| 5. C3×#63641 | C2 | semidirect |
| 6. (C2×D3)⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 7. #11722020 | C2 | semidirect |
| 26. C2×C3×ΓL(1,𝔽25) | D3 | semidirect |
| 34. #63641 | D3 | semidirect |
| 53. C32×C3⋊C8 | D4 | semidirect |
| 88. C2×C3⋊(C3⋊D3) | M16 | semidirect |
| 100. C2×ΓL(1,𝔽25) | C3⋊D3 | semidirect |
| 151. C3×C3⋊C8 | #67 | semidirect |
| 227. C33 | #435 | semidirect |
| 266. C3⋊C8 | #638 | semidirect |
| 328. C32 | #4836 | semidirect |
| 329. C32 | #5127 | semidirect |
| 374. C3 | #10590738 | semidirect |
| 375. C3 | #10592826 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×ΓL(1,𝔽25) | 2 |
| C4×#6291 | 2 |
| C2×#88785 | 2 |
| #11722190 | 2 |
| C3×#63641 | 2 |
| (C2×D3)⋊(C3⋊(C3⋊C8)) | 2 |
| #11722020 | 2 |
| #10592826 | 3 |
| #10590738 | 3 |