Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
818 conjugacy classes of subgroups; only the 218 normal subgroups are shown.
This group has 818 conjugacy classes of subgroups — too many to draw. Only its 218 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. C2×#63770 | C2 | direct (N × H) |
| 12. #63770 | C22 | direct (N × H) |
| 64. C22×C32 | #108 | semidirect |
| 98. C2×C32 | C2×#108 | semidirect |
| 126. C32 | C22×#108 | semidirect |
| 151. C22 | #63770 | direct (N × H) |
| 160. C2 | C2×#63770 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3788 | 2 |
| C22×C8×C3⋊D3 | 2 |
| C2×#63770 | 2 |
| C22×#108 | 9 |