Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
381 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 381 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 |
|---|---|---|
| 3. #10590818 | C2 | semidirect |
| 4. C2×#63551 | C2 | semidirect |
| 6. #10589133 | C2 | semidirect |
| 7. #10589119 | C2 | semidirect |
| 288. C32 | #2211 | semidirect |
| 329. C3 | #69205 | semidirect |
| 330. C3 | #71478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592854 | 2 |
| C2×C3×#827 | 2 |
| #10590818 | 2 |
| C2×#63551 | 2 |
| C3×#4562 | 2 |
| #10589133 | 2 |
| #10589119 | 2 |
| #71478 | 3 |
| #69205 | 3 |