Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
543 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 543 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 2. #10589623 | C2 | semidirect |
| 3. #10588819 | C2 | semidirect |
| 4. C2×#63383 | C2 | semidirect |
| 5. #10588685 | C2 | semidirect |
| 6. C9×H(3,ℤ/4) | C2 | semidirect |
| 7. #10588210 | C2 | semidirect |
| 20. #63437 | C4 | semidirect |
| 21. #63436 | C4 | semidirect |
| 46. C2×D36 | C2×C4 | semidirect |
| 50. C2×Dic18 | C2×C4 | semidirect |
| 58. C42×C9 | C2×C4 | semidirect |
| 59. C42×C9 | D4 | semidirect |
| 64. C4×Dic9 | D4 | semidirect |
| 124. H(3,ℤ/4) | D9 | semidirect |
| 266. C42 | C4×D9 | semidirect |
| 267. C42 | D36 | semidirect |
| 286. C9 | #1911 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589627 | 2 |
| #10589623 | 2 |
| #10588819 | 2 |
| C2×#63383 | 2 |
| #10588685 | 2 |
| C9×H(3,ℤ/4) | 2 |
| #10588210 | 2 |
| #68705 | 3 |