Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
234 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 97 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. #10593255 | C2 | semidirect |
| 4. #10593254 | C2 | semidirect |
| 7. #64218 | C4 | semidirect |
| 8. #64214 | C4 | semidirect |
| 24. #3771 | C2×C4 | semidirect |
| 65. #157 | M32 | semidirect |
| 119. C32 | C4×M32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596481 | 2 |
| C2×C8×#157 | 2 |
| #10593255 | 2 |
| #10593254 | 2 |
| C4×M32 | 9 |