Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1143 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 1143 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×#63710 | C2 | semidirect |
| 2. C9×#535 | C2 | semidirect |
| 3. #10589925 | C2 | semidirect |
| 4. C2×#63391 | C2 | semidirect |
| 5. #10588757 | C2 | semidirect |
| 6. #10588741 | C2 | semidirect |
| 7. #10588685 | C2 | semidirect |
| 9. C2×C9×#41 | C22 | semidirect |
| 18. C9×#127 | C22 | semidirect |
| 19. C9×#124 | C22 | semidirect |
| 22. C9×#117 | C22 | semidirect |
| 26. #63505 | C22 | semidirect |
| 27. #63495 | C22 | semidirect |
| 28. C2×#3667 | C22 | semidirect |
| 29. #63391 | C22 | semidirect |
| 30. #63364 | C22 | semidirect |
| 42. C2×Q8×C9 | C23 | semidirect |
| 49. C2×D4×C9 | C23 | semidirect |
| 63. #3697 | D4 | semidirect |
| 65. C2×D36 | D4 | semidirect |
| 67. C2×Dic18 | D4 | semidirect |
| 71. C42×C9 | C23 | semidirect |
| 77. #3667 | C23 | semidirect |
| 139. #535 | D9 | semidirect |
| 208. C2×#41 | C2×D9 | semidirect |
| 218. #127 | C2×D9 | semidirect |
| 219. #124 | C2×D9 | semidirect |
| 222. #117 | C2×D9 | semidirect |
| 278. C2×Q8 | C22×D9 | semidirect |
| 292. C2×D4 | C22×D9 | semidirect |
| 307. C42 | C22×D9 | semidirect |
| 326. C9 | #3019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63710 | 2 |
| C9×#535 | 2 |
| #10589925 | 2 |
| C2×#63391 | 2 |
| #10588757 | 2 |
| #10588741 | 2 |
| #10588685 | 2 |
| #83394 | 3 |