Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
681 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 681 conjugacy classes of subgroups — too many to draw. Only its 96 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. C3×#5116 | C2 | semidirect |
| 3. C2×#63549 | C2 | semidirect |
| 4. C3×#4549 | C2 | semidirect |
| 5. #10589116 | C2 | semidirect |
| 14. C2×C3×Dic12 | C22 | semidirect |
| 15. C3×#818 | C22 | semidirect |
| 17. C2×C3×C3⋊C16 | C22 | semidirect |
| 24. #5116 | D3 | semidirect |
| 27. #4549 | D3 | semidirect |
| 58. C2×Dic12 | C2×D3 | semidirect |
| 72. #818 | C2×D3 | semidirect |
| 74. C2×C3⋊C16 | C2×D3 | semidirect |
| 149. C22×C32 | SD32 | semidirect |
| 252. C22×C3 | #800 | semidirect |
| 253. C22×C3 | #828 | semidirect |
| 281. C32 | #2187 | semidirect |
| 321. C22 | #63549 | semidirect |
| 329. C3 | #69110 | semidirect |
| 330. C3 | #71085 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3745 | 2 |
| C3×#5116 | 2 |
| C2×#63549 | 2 |
| C3×#4549 | 2 |
| #10589116 | 2 |
| #71085 | 3 |
| #69110 | 3 |