Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
471 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 471 conjugacy classes of subgroups — too many to draw. Only its 74 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. #10594680 | C2 | semidirect |
| 2. C3×#4897 | C2 | semidirect |
| 3. C2×#63546 | C2 | semidirect |
| 4. #10590630 | C2 | semidirect |
| 5. #10589361 | C2 | semidirect |
| 6. C3×#4497 | C2 | semidirect |
| 7. #10589112 | C2 | semidirect |
| 14. C2×C3×D24 | C22 | semidirect |
| 20. C32×#108 | C22 | semidirect |
| 21. #63639 | C22 | semidirect |
| 23. C2×C3×C3⋊C16 | C22 | semidirect |
| 34. #4897 | D3 | semidirect |
| 38. #4497 | D3 | semidirect |
| 89. C2×D24 | C2×D3 | semidirect |
| 93. C3×#108 | C2×D3 | semidirect |
| 94. C3×#108 | C2×D3 | semidirect |
| 105. C2×C3⋊C16 | C2×D3 | semidirect |
| 224. #108 | D32 | semidirect |
| 341. C32 | #2192 | semidirect |
| 393. C3 | #69242 | semidirect |
| 394. C3 | #71094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10594680 | 2 |
| C3×#4897 | 2 |
| C2×#63546 | 2 |
| #10590630 | 2 |
| #10589361 | 2 |
| C3×#4497 | 2 |
| #10589112 | 2 |
| #71094 | 3 |
| #69242 | 3 |