Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1080 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 237 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. #10592920 | C2 | semidirect |
| 3. C2×#63659 | C2 | semidirect |
| 4. C2×#63641 | C2 | semidirect |
| 5. #10589417 | C2 | semidirect |
| 80. C2×C3⋊Dic3 | D8 | semidirect |
| 211. C32 | #2054 | semidirect |
| 262. C3 | #72040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×D8 | 2 |
| #10592920 | 2 |
| C2×#63659 | 2 |
| C2×#63641 | 2 |
| #10589417 | 2 |
| #72040 | 3 |