Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
849 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 849 conjugacy classes of subgroups — too many to draw. Only its 168 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. C2×C8×C3⋊Dic3 | C2 | semidirect |
| 3. C2×C3×#821 | C2 | semidirect |
| 4. #10591323 | C2 | semidirect |
| 5. C2×#63576 | C2 | semidirect |
| 15. C2×#3713 | C4 | semidirect |
| 22. C2×#821 | D3 | semidirect |
| 84. C2×C3⋊Dic3 | D8 | semidirect |
| 92. C3⋊(C3⋊C8) | C22⋊C4 | semidirect |
| 275. C32 | #1970 | semidirect |
| 328. C3 | #70190 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3713 | 2 |
| C2×C8×C3⋊Dic3 | 2 |
| C2×C3×#821 | 2 |
| #10591323 | 2 |
| C2×#63576 | 2 |
| #70190 | 3 |