Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
384 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 78 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. #10588788 | C2 | semidirect |
| 3. C2×#63359 | C2 | semidirect |
| 4. C9×C22⋊C16 | C2 | semidirect |
| 5. #10588186 | C2 | semidirect |
| 13. C2×Dic36 | C22 | semidirect |
| 14. C2×C9×C16 | C22 | semidirect |
| 15. #63378 | C22 | semidirect |
| 75. C22⋊C16 | D9 | semidirect |
| 96. C22×C9 | SD32 | semidirect |
| 115. C2×C16 | C2×D9 | semidirect |
| 172. C9 | #2187 | semidirect |
| 202. C22 | #63359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D72 | 2 |
| #10588788 | 2 |
| C2×#63359 | 2 |
| C9×C22⋊C16 | 2 |
| #10588186 | 2 |
| #69110 | 3 |