Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
594 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 185 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 |
|---|---|---|
| 4. #10592381 | C2 | semidirect |
| 5. #10592380 | C2 | semidirect |
| 6. #10592379 | C2 | semidirect |
| 7. C32×#322 | C2 | semidirect |
| 28. C3×#322 | D3 | semidirect |
| 76. C32×C8 | SD16 | semidirect |
| 83. #322 | C3⋊D3 | semidirect |
| 140. C3×C8 | #204 | semidirect |
| 173. C32 | #1714 | semidirect |
| 189. C8 | #3744 | semidirect |
| 204. C3 | #68090 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592393 | 2 |
| #10592392 | 2 |
| #10592381 | 2 |
| #10592380 | 2 |
| #10592379 | 2 |
| C32×#322 | 2 |
| #68090 | 3 |