Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
522 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 98 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×C9×#137 | C2 | semidirect |
| 3. #10589918 | C2 | semidirect |
| 4. #10588920 | C2 | semidirect |
| 5. #10588906 | C2 | semidirect |
| 6. #10588819 | C2 | semidirect |
| 7. #10588232 | C2 | semidirect |
| 146. C2×#137 | D9 | semidirect |
| 341. C9 | #2009 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#137 | 2 |
| #10589925 | 2 |
| #10589918 | 2 |
| #10588920 | 2 |
| #10588906 | 2 |
| #10588819 | 2 |
| #10588232 | 2 |
| #72111 | 3 |