Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1176 conjugacy classes of subgroups; only the 337 normal subgroups are shown.
This group has 1176 conjugacy classes of subgroups — too many to draw. Only its 337 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. C32×#423 | C2 | semidirect |
| 4. M16×C3⋊Dic3 | C2 | semidirect |
| 5. #10592623 | C2 | semidirect |
| 6. #10592539 | C2 | semidirect |
| 17. C32×C4⋊C8 | C22 | semidirect |
| 19. #63642 | C22 | semidirect |
| 20. C8×C3⋊Dic3 | C22 | semidirect |
| 21. C4⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 23. C3×#423 | D3 | semidirect |
| 57. C3×C4⋊C8 | C2×D3 | semidirect |
| 84. #423 | C3⋊D3 | semidirect |
| 128. C4⋊C8 | C2×C3⋊D3 | semidirect |
| 186. C32 | #2921 | semidirect |
| 222. C3 | #79039 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64081 | 2 |
| C32×#423 | 2 |
| #10592825 | 2 |
| M16×C3⋊Dic3 | 2 |
| #10592623 | 2 |
| #10592539 | 2 |
| #79039 | 3 |