Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
410 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 410 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 |
|---|---|---|
| 1. C2×C3×C8×D9 | C2 | semidirect |
| 3. C2×#88420 | C2 | semidirect |
| 4. #11720537 | C2 | semidirect |
| 5. C9×(C2×D3)⋊C8 | C2 | semidirect |
| 6. (C2×D9)⋊(C3⋊C8) | C2 | semidirect |
| 7. #11720275 | C2 | semidirect |
| 32. C2×C8×D9 | D3 | semidirect |
| 53. C3×C9⋊C8 | D4 | semidirect |
| 91. C2×C3×D9 | M16 | semidirect |
| 107. (C2×D3)⋊C8 | D9 | semidirect |
| 149. C9⋊C8 | #67 | semidirect |
| 205. C2×D9 | ΓL(1,𝔽25) | semidirect |
| 223. C3×C9 | #435 | semidirect |
| 320. C9 | #5111 | semidirect |
| 364. C3 | #10588410 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C8×D9 | 2 |
| C4×#6194 | 2 |
| C2×#88420 | 2 |
| #11720537 | 2 |
| C9×(C2×D3)⋊C8 | 2 |
| (C2×D9)⋊(C3⋊C8) | 2 |
| #11720275 | 2 |
| #10590723 | 3 |
| #10588410 | 3 |