Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
798 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 1. C22×#3745 | C2 | semidirect |
| 2. #10592814 | C2 | semidirect |
| 3. C2×#63626 | C2 | semidirect |
| 4. C32×C22⋊C16 | C2 | semidirect |
| 5. #10589375 | C2 | semidirect |
| 13. C2×#3745 | C22 | semidirect |
| 14. C2×C32×C16 | C22 | semidirect |
| 16. #63645 | C22 | semidirect |
| 21. C3×C22⋊C16 | D3 | semidirect |
| 39. #3745 | D4 | semidirect |
| 49. C2×C3×C16 | C2×D3 | semidirect |
| 76. C22⋊C16 | C3⋊D3 | semidirect |
| 97. C22×C32 | D16 | semidirect |
| 118. C2×C16 | C2×C3⋊D3 | semidirect |
| 166. C22×C3 | D48 | semidirect |
| 179. C32 | #2184 | semidirect |
| 214. C22 | #63626 | semidirect |
| 220. C3 | #69108 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3745 | 2 |
| #10592814 | 2 |
| C2×#63626 | 2 |
| C32×C22⋊C16 | 2 |
| #10589375 | 2 |
| #69108 | 3 |