Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
342 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 88 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. #10588803 | C2 | semidirect |
| 4. C2×#63381 | C2 | semidirect |
| 6. #10588644 | C2 | semidirect |
| 7. C9×#343 | C2 | semidirect |
| 104. #343 | D9 | semidirect |
| 238. C9 | #2063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10588813 | 2 |
| C2×#63383 | 2 |
| #10588803 | 2 |
| C2×#63381 | 2 |
| C2×#63369 | 2 |
| #10588644 | 2 |
| C9×#343 | 2 |
| #68996 | 3 |