Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
288 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 117 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. #10589329 | C2 | semidirect |
| 3. #10589321 | C2 | semidirect |
| 16. C32×Q16 | C8 | semidirect |
| 18. C32×D8 | C8 | semidirect |
| 51. C3×Q16 | C3⋊C8 | semidirect |
| 53. C3×D8 | C3⋊C8 | semidirect |
| 91. Q16 | C3⋊(C3⋊C8) | semidirect |
| 93. D8 | C3⋊(C3⋊C8) | semidirect |
| 108. C32 | #1336 | semidirect |
| 130. C3 | #67767 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#443 | 2 |
| #10589329 | 2 |
| #10589321 | 2 |
| #67767 | 3 |