Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
698 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 127 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 |
|---|---|---|
| 1. C22×#3718 | C2 | semidirect |
| 3. C22×#3708 | C2 | semidirect |
| 4. C2×#63735 | C2 | direct (N × H) |
| 9. C2×#3718 | C22 | semidirect |
| 12. C2×#3708 | C22 | semidirect |
| 13. #63735 | C22 | direct (N × H) |
| 26. #3718 | C23 | semidirect |
| 29. #3708 | C23 | semidirect |
| 79. C22×C32 | SD32 | semidirect |
| 119. C2×C32 | C2×SD32 | semidirect |
| 150. C32 | C22×SD32 | semidirect |
| 171. C22 | #63735 | direct (N × H) |
| 179. C2 | C2×#63735 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3718 | 2 |
| C22×#3713 | 2 |
| C22×#3708 | 2 |
| C2×#63735 | 2 |
| C22×SD32 | 9 |