Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 133 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×C9×Q16 | C2 | semidirect |
| 4. #11720581 | C2 | semidirect |
| 5. #11720535 | C2 | semidirect |
| 24. C2×C9×Q16 | D3 | semidirect |
| 71. C2×C3×Q16 | D9 | semidirect |
| 144. C2×Q16 | C3⋊D9 | semidirect |
| 148. C3×C9 | #473 | semidirect |
| 203. C9 | #5192 | semidirect |
| 228. C3 | #10588872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C9×Q16 | 2 |
| #11721853 | 2 |
| #11721770 | 2 |
| #11720581 | 2 |
| #11720535 | 2 |
| #10592891 | 3 |
| #10588872 | 3 |