Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
666 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 666 conjugacy classes of subgroups — too many to draw. Only its 110 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. #10589623 | C2 | semidirect |
| 3. #10588813 | C2 | semidirect |
| 4. C2×#63383 | C2 | semidirect |
| 5. #10588682 | C2 | semidirect |
| 6. C9×#339 | C2 | semidirect |
| 7. #10588201 | C2 | semidirect |
| 20. #63436 | C4 | semidirect |
| 48. C2×D36 | C2×C4 | semidirect |
| 54. C9×C4⋊C4 | D4 | semidirect |
| 58. C42×C9 | C2×C4 | semidirect |
| 61. C4⋊Dic9 | D4 | semidirect |
| 120. #339 | D9 | semidirect |
| 253. C4⋊C4 | D36 | semidirect |
| 260. C42 | C4×D9 | semidirect |
| 280. C9 | #1887 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10589623 | 2 |
| C2×#63436 | 2 |
| #10588813 | 2 |
| C2×#63383 | 2 |
| #10588682 | 2 |
| C9×#339 | 2 |
| #10588201 | 2 |
| #68760 | 3 |