Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
374 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 60 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. C22×C3×#733 | C2 | semidirect |
| 2. C2×C3×#733⋊C2 | C2 | semidirect |
| 3. C3×#733⋊C4 | C2 | semidirect |
| 6. #10619685 | C3 | direct (N × H) |
| 18. C22×#733 | C2×C3 | semidirect |
| 19. C2×#733⋊C2 | C2×C3 | semidirect |
| 20. #733⋊C4 | C2×C3 | semidirect |
| 21. C3×#733 | D4 | semidirect |
| 69. #733 | C3×D4 | semidirect |
| 165. C22×C3 | #733⋊C2 | semidirect |
| 197. C22 | C3×#733⋊C2 | semidirect |
| 202. C3 | #10619685 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#733 | 2 |
| C2×C3×#733⋊C2 | 2 |
| C3×#733⋊C4 | 2 |
| C3×#611⋊C3 | 3 |
| C32×#611 | 3 |
| #10619685 | 3 |