Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
722 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 722 conjugacy classes of subgroups — too many to draw. Only its 167 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 |
|---|---|---|
| 6. #10593551 | C2 | direct (N × H) |
| 127. C2×C32 | #400 | semidirect |
| 130. C3⋊D3 | #400 | semidirect |
| 170. C32 | C2×#400 | semidirect |
| 228. C2 | #10593551 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#157 | 2 |
| C22×#3777 | 2 |
| C2×#63781 | 2 |
| C2×#63747 | 2 |
| #10593551 | 2 |
| C2×#400 | 9 |