Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
343 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 343 conjugacy classes of subgroups — too many to draw. Only its 90 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. C3×#4873 | C2 | semidirect |
| 4. #10589355 | C2 | semidirect |
| 6. #10589118 | C2 | semidirect |
| 7. #10589103 | C2 | semidirect |
| 21. #63547 | C4 | semidirect |
| 26. #4873 | D3 | semidirect |
| 48. C3×Dic12 | C2×C4 | semidirect |
| 52. C3⋊(C3⋊C16) | C2×C4 | semidirect |
| 134. Dic12 | C4×D3 | semidirect |
| 248. C32 | #2175 | semidirect |
| 287. C3 | #69176 | semidirect |
| 288. C3 | #70913 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4873 | 2 |
| Dic3×D24 | 2 |
| C2×#63547 | 2 |
| #10589355 | 2 |
| C3×#4491 | 2 |
| #10589118 | 2 |
| #10589103 | 2 |
| #70913 | 3 |
| #69176 | 3 |