Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
310 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 56 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. #10593821 | C2 | semidirect |
| 3. D4⋊#622 | C2 | semidirect |
| 4. #10590170 | C2 | semidirect |
| 5. #10590168 | C2 | semidirect |
| 47. C32×C8 | M16 | semidirect |
| 117. C32 | #1594 | semidirect |
| 131. C8 | #3792 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10593821 | 2 |
| D8×C3⋊Dic3 | 2 |
| D4⋊#622 | 2 |
| #10590170 | 2 |
| #10590168 | 2 |
| #1594 | 9 |