Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
620 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 117 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. C2×C9×ΓL(1,𝔽25) | C2 | semidirect |
| 3. #11720906 | C2 | semidirect |
| 4. #11720543 | C2 | semidirect |
| 5. C3×#63380 | C2 | semidirect |
| 6. #11720284 | C2 | semidirect |
| 7. #11720283 | C2 | semidirect |
| 16. D3×D36 | C4 | semidirect |
| 17. C2×C3×C8×C9 | C22 | semidirect |
| 18. C4⋊(C3⋊Dic9) | C22 | semidirect |
| 19. C3×C4⋊Dic9 | C22 | semidirect |
| 20. C2×C9×C3⋊C8 | C22 | semidirect |
| 38. #63380 | D3 | semidirect |
| 85. C2×C8×C9 | C2×D3 | semidirect |
| 89. C4⋊Dic9 | C2×D3 | semidirect |
| 111. C2×ΓL(1,𝔽25) | D9 | semidirect |
| 191. C2×C3×C8 | C2×D9 | semidirect |
| 202. C2×C3⋊C8 | C2×D9 | semidirect |
| 250. C3×C9 | #418 | semidirect |
| 320. C2×C8 | D3×D9 | semidirect |
| 366. C9 | #4770 | semidirect |
| 419. C3 | #10588813 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D3×D36 | 2 |
| C2×C9×ΓL(1,𝔽25) | 2 |
| #11720906 | 2 |
| #11720543 | 2 |
| C3×#63380 | 2 |
| #11720284 | 2 |
| #11720283 | 2 |
| #10590939 | 3 |
| #10588813 | 3 |