Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
610 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 3. #10593544 | C2 | semidirect |
| 4. #10593543 | C2 | semidirect |
| 7. C2×#3792 | C4 | semidirect |
| 14. #64283 | C4 | semidirect |
| 16. C2×#3788 | C4 | semidirect |
| 18. #63746 | C22 | semidirect |
| 19. #63745 | C22 | semidirect |
| 34. #3792 | C2×C4 | semidirect |
| 35. C2×#622 | C2×C4 | semidirect |
| 40. #3788 | C2×C4 | semidirect |
| 41. #3787 | C2×C4 | semidirect |
| 188. C32 | #2911 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64286 | 2 |
| C2×#64283 | 2 |
| #10593544 | 2 |
| #10593543 | 2 |
| #2911 | 9 |