Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
670 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 78 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×#63783 | C2 | semidirect |
| 3. C42×#157 | C2 | semidirect |
| 4. #10593728 | C2 | semidirect |
| 9. C32×#127 | C4 | semidirect |
| 11. #64145 | C4 | semidirect |
| 14. #64078 | C4 | semidirect |
| 31. C4×#157 | D4 | semidirect |
| 89. C32×C4 | #104 | semidirect |
| 98. #127 | #157 | semidirect |
| 158. C32 | #1962 | semidirect |
| 192. C4 | #63783 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596187 | 2 |
| C2×#63783 | 2 |
| C42×#157 | 2 |
| #10593728 | 2 |
| #1962 | 9 |