Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
275 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 275 conjugacy classes of subgroups — too many to draw. Only its 58 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. #10589423 | C2 | semidirect |
| 3. C3×#4553 | C2 | semidirect |
| 9. C2×C3×D24 | C4 | semidirect |
| 11. C3×#817 | C4 | semidirect |
| 19. #4553 | D3 | semidirect |
| 43. C2×D24 | Dic3 | semidirect |
| 48. #817 | Dic3 | semidirect |
| 197. C32 | #1339 | semidirect |
| 234. C3 | #67534 | semidirect |
| 235. C3 | #67778 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5135 | 2 |
| #10589423 | 2 |
| C3×#4553 | 2 |
| #67778 | 3 |
| #67534 | 3 |