Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
222 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 93 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. #10589371 | C2 | semidirect |
| 3. #10589365 | C2 | semidirect |
| 6. C32×Q32 | C4 | semidirect |
| 8. C32×D16 | C4 | semidirect |
| 25. C3×Q32 | Dic3 | semidirect |
| 27. C3×D16 | Dic3 | semidirect |
| 57. Q32 | C3⋊Dic3 | semidirect |
| 59. D16 | C3⋊Dic3 | semidirect |
| 88. C32 | #1418 | semidirect |
| 106. C3 | #67828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#508 | 2 |
| #10589371 | 2 |
| #10589365 | 2 |
| #67828 | 3 |