Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
924 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 173 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. #10592718 | C2 | semidirect |
| 4. #10592706 | C2 | semidirect |
| 5. #10589410 | C2 | semidirect |
| 6. D4⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 7. D4⋊(C3⋊(C3⋊C8)) | C2 | semidirect |
| 18. #64078 | C22 | semidirect |
| 23. C4⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 24. C4⋊(C3⋊(C3⋊C8)) | C22 | semidirect |
| 25. C4×C3⋊(C3⋊C8) | C22 | semidirect |
| 94. C32×D4 | SD16 | semidirect |
| 196. C3×D4 | #214 | semidirect |
| 264. C32 | #1639 | semidirect |
| 283. D4 | #3754 | semidirect |
| 322. C3 | #71908 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×D42 | 2 |
| #10592769 | 2 |
| #10592718 | 2 |
| #10592706 | 2 |
| #10589410 | 2 |
| D4⋊(C3⋊(C3⋊C8)) | 2 |
| #71908 | 3 |