Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
317 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 317 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 2. C3×#5106 | C2 | semidirect |
| 3. #10589415 | C2 | semidirect |
| 4. #10589142 | C2 | semidirect |
| 5. #10589140 | C2 | semidirect |
| 6. #10589114 | C2 | semidirect |
| 7. #10589114 | C2 | semidirect |
| 24. #5106 | D3 | semidirect |
| 259. C32 | #2234 | semidirect |
| 303. C3 | #70653 | semidirect |
| 304. C3 | #71070 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5115 | 2 |
| C3×#5106 | 2 |
| #10589415 | 2 |
| #10589142 | 2 |
| #10589140 | 2 |
| #10589114 | 2 |
| #71070 | 3 |
| #70653 | 3 |