Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
376 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 21. #63784 | C4 | semidirect |
| 74. C32×Q8 | C4⋊C4 | semidirect |
| 88. #634 | C4⋊C4 | semidirect |
| 209. C32 | #1865 | semidirect |
| 216. Q8 | #3777 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#157 | 2 |
| C2×#63784 | 2 |
| #10593554 | 2 |
| C2×#63745 | 2 |
| #10590093 | 2 |
| #10590090 | 2 |
| #1865 | 9 |