Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
609 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 609 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 1. #10589935 | C2 | semidirect |
| 2. C2×#63512 | C2 | semidirect |
| 3. C2×#63470 | C2 | semidirect |
| 4. C2×C9×#104 | C2 | semidirect |
| 5. #10588619 | C2 | semidirect |
| 6. C2×#63364 | C2 | semidirect |
| 7. #10588234 | C2 | semidirect |
| 63. C2×D36 | D4 | semidirect |
| 67. C9×M16 | D4 | semidirect |
| 80. #3667 | D4 | semidirect |
| 156. C2×#104 | D9 | semidirect |
| 337. M16 | #611 | semidirect |
| 372. C9 | #2006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589935 | 2 |
| C2×#63512 | 2 |
| C2×#63470 | 2 |
| C2×C9×#104 | 2 |
| #10588619 | 2 |
| C2×#63364 | 2 |
| #10588234 | 2 |
| #70392 | 3 |