Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
553 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 553 conjugacy classes of subgroups — too many to draw. Only its 124 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. #10590707 | C2 | semidirect |
| 3. C2×#63543 | C2 | semidirect |
| 4. #10589428 | C2 | semidirect |
| 5. C3×#4562 | C2 | semidirect |
| 6. #10589115 | C2 | semidirect |
| 7. #10589114 | C2 | semidirect |
| 14. C3×D3×D8 | C4 | semidirect |
| 18. #63645 | C22 | semidirect |
| 19. C2×C3⋊(C3⋊C16) | C22 | semidirect |
| 20. C3×#818 | C22 | semidirect |
| 21. C2×C3×C3⋊C16 | C22 | semidirect |
| 36. #4562 | D3 | semidirect |
| 75. D3×D8 | Dic3 | semidirect |
| 84. #818 | C2×D3 | semidirect |
| 90. C2×C3⋊C16 | C2×D3 | semidirect |
| 314. C32 | #2140 | semidirect |
| 368. C3 | #69190 | semidirect |
| 369. C3 | #72033 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D3×D8 | 2 |
| #10590707 | 2 |
| C2×#63543 | 2 |
| #10589428 | 2 |
| C3×#4562 | 2 |
| #10589115 | 2 |
| #10589114 | 2 |
| #72033 | 3 |
| #69190 | 3 |