Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
219 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 219 conjugacy classes of subgroups — too many to draw. Only its 76 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. #10588380 | C2 | semidirect |
| 3. C4×C9×C16 | C2 | semidirect |
| 4. #10588187 | C2 | semidirect |
| 5. #10588183 | C2 | semidirect |
| 14. Dic72 | C4 | semidirect |
| 15. #63359 | C4 | semidirect |
| 16. D144 | C4 | semidirect |
| 61. C4×C16 | D9 | semidirect |
| 124. C9 | #2178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10588584 | 2 |
| #10588380 | 2 |
| C4×C9×C16 | 2 |
| #10588187 | 2 |
| #10588183 | 2 |
| #69067 | 3 |