Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
221 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 221 conjugacy classes of subgroups — too many to draw. Only its 69 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×#64213 | C2 | semidirect |
| 3. #10593264 | C2 | semidirect |
| 4. C4⋊#3771 | C2 | semidirect |
| 5. C4×#3771 | C2 | semidirect |
| 24. #3771 | D4 | semidirect |
| 35. C4⋊(C3⋊D3) | C16 | semidirect |
| 55. C2×C3⋊D3 | C2×C16 | semidirect |
| 57. C32×C4 | C2×C16 | semidirect |
| 104. C32 | D4×C16 | semidirect |
| 129. C4 | #64213 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64213 | 2 |
| #10593749 | 2 |
| #10593264 | 2 |
| C4⋊#3771 | 2 |
| C4×#3771 | 2 |
| D4×C16 | 9 |