Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
319 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 319 conjugacy classes of subgroups — too many to draw. Only its 76 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. #10592824 | C2 | semidirect |
| 3. C3×#4553 | C2 | semidirect |
| 4. #10589136 | C2 | semidirect |
| 5. #10589127 | C2 | semidirect |
| 24. #4553 | D3 | semidirect |
| 211. C32 | #2238 | semidirect |
| 247. C3 | #69116 | semidirect |
| 248. C3 | #71088 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592824 | 2 |
| C3×#5135 | 2 |
| C3×#4553 | 2 |
| #10589136 | 2 |
| #10589127 | 2 |
| #71088 | 3 |
| #69116 | 3 |