Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1509 conjugacy classes of subgroups; only the 228 normal subgroups are shown.
This group has 1509 conjugacy classes of subgroups — too many to draw. Only its 228 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. C2×#64102 | C2 | semidirect |
| 2. C2×#63914 | C2 | semidirect |
| 3. C22×#3714 | C2 | semidirect |
| 4. C2×C3×#809 | C2 | semidirect |
| 5. C2×#63572 | C2 | semidirect |
| 6. #10590551 | C2 | direct (N × H) |
| 17. #64102 | C22 | semidirect |
| 20. #63914 | C22 | semidirect |
| 22. C2×#3714 | C22 | semidirect |
| 23. C3×#809 | C22 | semidirect |
| 24. #63572 | C22 | semidirect |
| 32. C2×#809 | D3 | semidirect |
| 42. C2×C4⋊(C3⋊D3) | D4 | semidirect |
| 91. #809 | C2×D3 | semidirect |
| 108. C2×C3⋊Dic3 | D8 | semidirect |
| 113. C4⋊(C3⋊D3) | C2×D4 | semidirect |
| 196. C3⋊Dic3 | C2×D8 | semidirect |
| 270. C2×C32 | #459 | semidirect |
| 340. C32 | C2×#459 | semidirect |
| 375. C2×C3 | #4786 | semidirect |
| 401. C3 | C2×#4786 | semidirect |
| 404. C2 | #10590551 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64102 | 2 |
| C2×#63914 | 2 |
| C22×#3714 | 2 |
| C2×C3×#809 | 2 |
| C2×#63572 | 2 |
| #10590551 | 2 |
| C2×#4786 | 3 |