Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
250 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 101 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. #10593263 | C2 | semidirect |
| 4. C4×#3771 | C2 | semidirect |
| 7. #64218 | C4 | direct (N × H) |
| 23. #3771 | C2×C4 | semidirect |
| 61. C32×C4 | M32 | semidirect |
| 64. C3⋊Dic3 | M32 | semidirect |
| 116. C32 | C4×M32 | semidirect |
| 146. C4 | #64218 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64218 | 2 |
| C2×C4×#622 | 2 |
| #10593263 | 2 |
| C4×#3771 | 2 |
| C4×M32 | 9 |