Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1178 conjugacy classes of subgroups; only the 338 normal subgroups are shown.
This group has 1178 conjugacy classes of subgroups — too many to draw. Only its 338 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 |
|---|---|---|
| 3. C2×#63777 | C2 | semidirect |
| 4. #10593723 | C2 | direct (N × H) |
| 8. C2×#3787 | C4 | semidirect |
| 15. #63777 | C22 | semidirect |
| 27. C2×#622 | C2×C4 | semidirect |
| 29. #3787 | C2×C4 | semidirect |
| 58. #622 | C22×C4 | semidirect |
| 80. C2×C3⋊D3 | #97 | semidirect |
| 115. C2×C32 | C2×#97 | semidirect |
| 118. C3⋊D3 | C2×#97 | semidirect |
| 147. C32 | C22×#97 | semidirect |
| 182. C2 | #10593723 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3787 | 2 |
| C2×C42×C3⋊D3 | 2 |
| C2×#63777 | 2 |
| #10593723 | 2 |
| C22×#97 | 9 |