Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
705 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 705 conjugacy classes of subgroups — too many to draw. Only its 180 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 |
|---|---|---|
| 14. C2×#3718 | C4 | semidirect |
| 72. C2×C32×C4 | Q16 | semidirect |
| 182. C2×C3×C4 | #216 | semidirect |
| 252. C32 | #1969 | semidirect |
| 265. C2×C4 | #3718 | semidirect |
| 297. C3 | #69677 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3718 | 2 |
| C2×C4×C3⋊(C3⋊C8) | 2 |
| C3×#4929 | 2 |
| C2×#63576 | 2 |
| C2×#63565 | 2 |
| #69677 | 3 |