Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
780 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 780 conjugacy classes of subgroups — too many to draw. Only its 209 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. C2×#63663 | C2 | semidirect |
| 3. #10589408 | C2 | direct (N × H) |
| 14. #63663 | C22 | semidirect |
| 140. C2×C32 | #355 | semidirect |
| 175. C32 | C2×#355 | semidirect |
| 200. C2×C3 | #4542 | semidirect |
| 215. C3 | C2×#4542 | semidirect |
| 219. C2 | #10589408 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#124 | 2 |
| C2×#63663 | 2 |
| #10589408 | 2 |
| C2×#4542 | 3 |