Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
513 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 513 conjugacy classes of subgroups — too many to draw. Only its 104 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. C22×#3674 | C2 | semidirect |
| 5. C2×#63394 | C2 | semidirect |
| 6. C2×#63382 | C2 | semidirect |
| 7. #10588231 | C2 | semidirect |
| 308. C9 | #2020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#137 | 2 |
| C2×#63511 | 2 |
| C22×#3674 | 2 |
| #10588912 | 2 |
| C2×#63394 | 2 |
| C2×#63382 | 2 |
| #10588231 | 2 |
| #72109 | 3 |