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. C2×C32×C4⋊C8 | C2 | semidirect |
| 3. C2×#63648 | C2 | semidirect |
| 4. #10592638 | C2 | semidirect |
| 5. #10589417 | C2 | semidirect |
| 19. C2×C3×C4⋊C8 | D3 | semidirect |
| 69. C2×C32×C4 | D8 | semidirect |
| 84. C2×C4⋊C8 | C3⋊D3 | semidirect |
| 151. C2×C3×C4 | D24 | semidirect |
| 211. C32 | #2054 | semidirect |
| 231. C2×C4 | #3745 | semidirect |
| 262. C3 | #70481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3745 | 2 |
| C2×C32×C4⋊C8 | 2 |
| C2×#63648 | 2 |
| #10592638 | 2 |
| #10589417 | 2 |
| #70481 | 3 |