Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1491 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 1491 conjugacy classes of subgroups — too many to draw. Only its 234 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. C23×D4×C9 | C2 | semidirect |
| 2. C2×#63495 | C2 | semidirect |
| 3. #10589893 | C2 | semidirect |
| 4. #10588898 | C2 | semidirect |
| 5. #10588897 | C2 | semidirect |
| 6. #10588896 | C2 | semidirect |
| 7. #10588887 | C2 | semidirect |
| 16. C2×#3697 | C22 | semidirect |
| 19. C2×#3673 | C22 | semidirect |
| 20. C2×#3672 | C22 | semidirect |
| 21. #63492 | C22 | semidirect |
| 24. #63488 | C22 | semidirect |
| 25. #63486 | C22 | semidirect |
| 26. C2×#3667 | C22 | semidirect |
| 27. #63392 | C22 | semidirect |
| 28. #63389 | C22 | semidirect |
| 47. C2×D4×C9 | D4 | semidirect |
| 57. C2×D36 | C23 | semidirect |
| 59. C2×Dic18 | C23 | semidirect |
| 65. C4⋊Dic9 | C23 | semidirect |
| 69. C2×C9⋊C8 | C23 | semidirect |
| 122. C23×D4 | D9 | semidirect |
| 172. C22×C9 | AGL(1,ℤ/8) | semidirect |
| 254. C2×D4 | #611 | semidirect |
| 290. C9 | #3003 | semidirect |
| 338. C22 | #63495 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D4×C9 | 2 |
| C2×#63495 | 2 |
| #10589893 | 2 |
| #10588898 | 2 |
| #10588897 | 2 |
| #10588896 | 2 |
| #10588887 | 2 |
| #84038 | 3 |