Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
774 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 215 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 |
|---|---|---|
| 4. #10593553 | C2 | semidirect |
| 5. C4×#3777 | C2 | semidirect |
| 6. #10593545 | C2 | semidirect |
| 12. C2×C4×#157 | C4 | semidirect |
| 55. C2×C32×C4 | C4⋊C4 | semidirect |
| 58. C2×C3⋊Dic3 | C4⋊C4 | semidirect |
| 61. C4×C3⋊D3 | C4⋊C4 | semidirect |
| 62. C4×C3⋊D3 | C4⋊C4 | semidirect |
| 94. #157 | #117 | semidirect |
| 170. C32 | #2285 | semidirect |
| 193. C2×C4 | #3777 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64286 | 2 |
| C22×C4×#157 | 2 |
| #10593568 | 2 |
| #10593553 | 2 |
| C4×#3777 | 2 |
| #10593545 | 2 |
| #2285 | 9 |