Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1836 conjugacy classes of subgroups; only the 370 normal subgroups are shown.
This group has 1836 conjugacy classes of subgroups — too many to draw. Only its 370 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. C24×C4×C9 | C2 | semidirect |
| 3. C2×C4×#611 | C2 | semidirect |
| 4. #10588927 | C2 | semidirect |
| 5. #10588893 | C2 | semidirect |
| 6. #10588890 | C2 | semidirect |
| 7. C4×#3676 | C2 | semidirect |
| 14. C22×C4×D9 | C22 | semidirect |
| 15. #63515 | C4 | direct (N × H) |
| 20. C2×(C2×D9)⋊C4 | C22 | semidirect |
| 21. C2×Dic9⋊C4 | C22 | semidirect |
| 22. C2×C4×Dic9 | C22 | semidirect |
| 23. C9⋊#95 | C22 | semidirect |
| 33. C24×C9 | C2×C4 | semidirect |
| 40. C22×C4×C9 | D4 | semidirect |
| 45. C2×#611 | C2×C4 | semidirect |
| 52. #3676 | C2×C4 | semidirect |
| 83. C22×D9 | C22×C4 | semidirect |
| 95. C2×Dic9 | C22×C4 | semidirect |
| 97. C24×C4 | D9 | semidirect |
| 134. C22×C9 | C4×D4 | semidirect |
| 142. C4×C9 | #120 | semidirect |
| 194. C24 | C4×D9 | semidirect |
| 207. C22×C4 | #611 | semidirect |
| 233. C9 | C4×#120 | semidirect |
| 272. C22 | C4×#611 | semidirect |
| 280. C4 | #63515 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C4×C9 | 2 |
| C2×#63515 | 2 |
| C2×C4×#611 | 2 |
| #10588927 | 2 |
| #10588893 | 2 |
| #10588890 | 2 |
| C4×#3676 | 2 |
| C4×#953 | 3 |