Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
594 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 145 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. #10592779 | C2 | semidirect |
| 3. #10592777 | C2 | semidirect |
| 6. #10592380 | C2 | semidirect |
| 7. #10589320 | C2 | semidirect |
| 76. C3⋊(C3⋊C8) | SD16 | semidirect |
| 173. C32 | #1714 | semidirect |
| 204. C3 | #71257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#492 | 2 |
| #10592779 | 2 |
| #10592777 | 2 |
| #10592775 | 2 |
| #10592769 | 2 |
| #10592380 | 2 |
| #10589320 | 2 |
| #71257 | 3 |