Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
492 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 177 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. #3756 | C8 | direct (N × H) |
| 77. C32×C8 | Q16 | semidirect |
| 144. C3×C8 | #216 | semidirect |
| 179. C32 | C8×Q16 | semidirect |
| 197. C8 | #3756 | direct (N × H) |
| 211. C3 | C8×#216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C8×Q8 | 2 |
| C4×#3756 | 2 |
| C8×#634 | 2 |
| #10589401 | 2 |
| #10589350 | 2 |
| #10589345 | 2 |
| C8×C3⋊(C3⋊C8) | 2 |
| C8×#216 | 3 |