Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
521 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 521 conjugacy classes of subgroups — too many to draw. Only its 156 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 |
|---|---|---|
| 12. #63630 | C4 | semidirect |
| 13. #63578 | C4 | semidirect |
| 14. #63576 | C4 | semidirect |
| 15. #63574 | C4 | semidirect |
| 208. C32 | #1773 | semidirect |
| 242. C3 | #68742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63630 | 2 |
| C2×#63578 | 2 |
| #10591138 | 2 |
| #10591057 | 2 |
| C3×#4523 | 2 |
| #68742 | 3 |