Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
561 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 561 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 3. C2×#63551 | C2 | semidirect |
| 5. #10589119 | C2 | semidirect |
| 147. C22×C32 | Q32 | semidirect |
| 240. C22×C3 | Dic24 | semidirect |
| 241. C22×C3 | #829 | semidirect |
| 260. C32 | #2188 | semidirect |
| 291. C22 | #63551 | semidirect |
| 300. C3 | #69113 | semidirect |
| 301. C3 | #71087 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3746 | 2 |
| C3×#5116 | 2 |
| C2×#63551 | 2 |
| C3×#4549 | 2 |
| #10589119 | 2 |
| #71087 | 3 |
| #69113 | 3 |