Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
360 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 2. #10592382 | C2 | semidirect |
| 3. C32×#364 | C2 | semidirect |
| 5. #10589379 | C2 | semidirect |
| 18. C3×#364 | D3 | semidirect |
| 59. #364 | C3⋊D3 | semidirect |
| 125. C32 | #2231 | semidirect |
| 148. C3 | #69308 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592399 | 2 |
| #10592382 | 2 |
| C32×#364 | 2 |
| #10589384 | 2 |
| #10589379 | 2 |
| #69308 | 3 |