Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
675 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 675 conjugacy classes of subgroups — too many to draw. Only its 100 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. #10592769 | C2 | semidirect |
| 3. #10590365 | C2 | semidirect |
| 4. #10590272 | C2 | semidirect |
| 5. C3×#4544 | C2 | semidirect |
| 6. #10589080 | C2 | semidirect |
| 7. #10589080 | C2 | semidirect |
| 13. #64078 | C22 | semidirect |
| 21. C4×C3⋊(C3⋊C8) | C22 | semidirect |
| 22. C3×C4⋊(C3⋊C8) | C22 | semidirect |
| 23. C3×C4⋊(C3⋊C8) | C22 | semidirect |
| 37. #4544 | D3 | semidirect |
| 103. C4⋊(C3⋊C8) | C2×D3 | semidirect |
| 104. C4⋊(C3⋊C8) | C2×D3 | semidirect |
| 132. C3×D12 | SD16 | semidirect |
| 304. D12 | #214 | semidirect |
| 403. C32 | #1639 | semidirect |
| 472. C3 | #68392 | semidirect |
| 473. C3 | #71908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5717 | 2 |
| #10592769 | 2 |
| #10590365 | 2 |
| #10590272 | 2 |
| C3×#4544 | 2 |
| #10589080 | 2 |
| #71908 | 3 |
| #68392 | 3 |