Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
594 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 1. C32×#459 | C2 | semidirect |
| 2. #10592772 | C2 | semidirect |
| 3. #10592714 | C2 | semidirect |
| 4. #10592711 | C2 | semidirect |
| 5. #10589410 | C2 | semidirect |
| 6. #10589351 | C2 | semidirect |
| 7. #10589346 | C2 | semidirect |
| 24. C3×#459 | D3 | semidirect |
| 93. C3⋊(C3⋊C8) | D8 | semidirect |
| 96. #459 | C3⋊D3 | semidirect |
| 222. C32 | #1687 | semidirect |
| 271. C3 | #71009 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#459 | 2 |
| #10592772 | 2 |
| #10592714 | 2 |
| #10592711 | 2 |
| #10589410 | 2 |
| #10589351 | 2 |
| #10589346 | 2 |
| #71009 | 3 |