Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
411 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 411 conjugacy classes of subgroups — too many to draw. Only its 86 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. #10592571 | C2 | semidirect |
| 2. #10590777 | C2 | semidirect |
| 4. C3×#4491 | C2 | semidirect |
| 5. C3×#4490 | C2 | semidirect |
| 6. #10589116 | C2 | semidirect |
| 7. #10589104 | C2 | semidirect |
| 21. #63546 | C4 | semidirect |
| 35. #4491 | D3 | semidirect |
| 36. #4490 | D3 | semidirect |
| 47. #3745 | C2×C4 | semidirect |
| 50. C3×D24 | C2×C4 | semidirect |
| 53. C3×C3⋊C16 | C2×C4 | semidirect |
| 145. D24 | C4×D3 | semidirect |
| 149. C3⋊C16 | C4×D3 | semidirect |
| 275. C32 | #2177 | semidirect |
| 320. C3 | #69177 | semidirect |
| 321. C3 | #69339 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592571 | 2 |
| #10590777 | 2 |
| C2×#63546 | 2 |
| C3×#4491 | 2 |
| C3×#4490 | 2 |
| #10589116 | 2 |
| #10589104 | 2 |
| #69339 | 3 |
| #69177 | 3 |