Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
210 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 56 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. C2×#63388 | C2 | semidirect |
| 5. C9×#362 | C2 | semidirect |
| 6. #10588195 | C2 | semidirect |
| 7. #10588170 | C2 | semidirect |
| 89. #362 | D9 | semidirect |
| 178. C9 | #2222 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10588872 | 2 |
| C2×#63388 | 2 |
| #10588587 | 2 |
| #10588576 | 2 |
| C9×#362 | 2 |
| #10588195 | 2 |
| #10588170 | 2 |
| #69270 | 3 |