Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
365 conjugacy classes of subgroups; only the 120 normal subgroups are shown.
This group has 365 conjugacy classes of subgroups — too many to draw. Only its 120 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 |
|---|---|---|
| 36. #3718 | C8 | direct (N × H) |
| 64. C32×C8 | Q16 | semidirect |
| 133. C3×C8 | #216 | semidirect |
| 172. C32 | C8×Q16 | semidirect |
| 185. C8 | #3718 | direct (N × H) |
| 201. C3 | C8×#216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C8×Dic6 | 2 |
| C4×#3718 | 2 |
| C8×C3⋊(C3⋊C8) | 2 |
| #10589100 | 2 |
| #10589083 | 2 |
| C8×#216 | 3 |