Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1047 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 1047 conjugacy classes of subgroups — too many to draw. Only its 184 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. C9×#536 | C2 | semidirect |
| 3. #10589925 | C2 | semidirect |
| 4. C2×#63394 | C2 | semidirect |
| 5. #10588775 | C2 | semidirect |
| 6. #10588742 | C2 | semidirect |
| 7. #10588685 | C2 | semidirect |
| 18. C9×C4⋊Q8 | C22 | semidirect |
| 19. C9×#124 | C22 | semidirect |
| 26. #63505 | C22 | semidirect |
| 27. #63495 | C22 | semidirect |
| 29. #63394 | C22 | semidirect |
| 30. #63364 | C22 | semidirect |
| 136. #536 | D9 | semidirect |
| 211. C4⋊Q8 | C2×D9 | semidirect |
| 212. #124 | C2×D9 | semidirect |
| 311. C9 | #3020 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63713 | 2 |
| C9×#536 | 2 |
| #10589925 | 2 |
| C2×#63394 | 2 |
| #10588775 | 2 |
| #10588742 | 2 |
| #10588685 | 2 |
| #83415 | 3 |