Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
365 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 365 conjugacy classes of subgroups — too many to draw. Only its 128 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 |
|---|---|---|
| 40. C3×Dic12 | C8 | semidirect |
| 76. C3⋊(C3⋊C8) | Q16 | semidirect |
| 112. Dic12 | C3⋊C8 | semidirect |
| 202. C32 | C8×Q16 | semidirect |
| 234. C3 | #68557 | semidirect |
| 235. C3 | Q16×C3⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×Dic12 | 2 |
| #10590250 | 2 |
| C8×C3⋊(C3⋊C8) | 2 |
| C3×#4458 | 2 |
| #10589083 | 2 |
| Q16×C3⋊C8 | 3 |
| #68557 | 3 |