Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1092 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 1092 conjugacy classes of subgroups — too many to draw. Only its 190 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×#63713 | C2 | semidirect |
| 2. C2×C9×#124 | C2 | semidirect |
| 3. C2×#63495 | C2 | semidirect |
| 4. C2×#63394 | C2 | semidirect |
| 5. #10588742 | C2 | direct (N × H) |
| 6. C2×#63364 | C2 | semidirect |
| 12. #63713 | C22 | semidirect |
| 18. C9×#124 | C22 | semidirect |
| 22. #63495 | C22 | semidirect |
| 26. #63394 | C22 | semidirect |
| 27. #63364 | C22 | semidirect |
| 126. C2×#124 | D9 | semidirect |
| 197. #124 | C2×D9 | semidirect |
| 237. C2×C9 | #454 | semidirect |
| 292. C9 | C2×#454 | semidirect |
| 351. C2 | #10588742 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63713 | 2 |
| C2×C9×#124 | 2 |
| C2×#63495 | 2 |
| C2×#63394 | 2 |
| #10588742 | 2 |
| C2×#63364 | 2 |
| C2×#5062 | 3 |