Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
498 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 141 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. C32×#498 | C2 | semidirect |
| 5. #10589413 | C2 | semidirect |
| 6. #10589412 | C2 | semidirect |
| 7. #10589323 | C2 | semidirect |
| 24. C3×#498 | D3 | semidirect |
| 80. C32×C8 | SD16 | semidirect |
| 84. #498 | C3⋊D3 | semidirect |
| 151. C3×C8 | #215 | semidirect |
| 189. C32 | #1671 | semidirect |
| 208. C8 | #3755 | semidirect |
| 225. C3 | #71344 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#498 | 2 |
| #10592783 | 2 |
| #10592782 | 2 |
| C8×C4⋊(C3⋊D3) | 2 |
| #10589413 | 2 |
| #10589412 | 2 |
| #10589323 | 2 |
| #71344 | 3 |