Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
634 conjugacy classes of subgroups; only the 242 normal subgroups are shown.
This group has 634 conjugacy classes of subgroups — too many to draw. Only its 242 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. #10593838 | C2 | direct (N × H) |
| 3. C2×#63773 | C2 | semidirect |
| 4. C22×#3708 | C2 | semidirect |
| 10. #63773 | C22 | semidirect |
| 13. C2×#3708 | C22 | semidirect |
| 83. C2×C32 | #504 | semidirect |
| 103. C32 | C2×#504 | semidirect |
| 125. C2 | #10593838 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64157 | 2 |
| #10593838 | 2 |
| C2×#63773 | 2 |
| C22×#3708 | 2 |
| C2×#504 | 9 |