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. C2×#63495 | C2 | semidirect |
| 2. #10589612 | C2 | semidirect |
| 3. C9×#390 | C2 | semidirect |
| 4. C2×#63364 | C2 | semidirect |
| 5. #10588207 | C2 | semidirect |
| 30. C2×D4×C9 | D4 | semidirect |
| 51. #3667 | D4 | semidirect |
| 100. #390 | D9 | semidirect |
| 209. C2×D4 | D36 | semidirect |
| 242. C9 | #2006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63495 | 2 |
| #10589612 | 2 |
| C9×#390 | 2 |
| C2×#63364 | 2 |
| #10588207 | 2 |
| #69664 | 3 |