Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
984 conjugacy classes of subgroups; only the 262 normal subgroups are shown.
This group has 984 conjugacy classes of subgroups — too many to draw. Only its 262 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×C9×C4⋊Q8 | C2 | semidirect |
| 2. C22×#3675 | C2 | semidirect |
| 4. #10588770 | C2 | direct (N × H) |
| 5. C2×C4×C9⋊C8 | C2 | semidirect |
| 11. C9×C4⋊Q8 | C22 | semidirect |
| 15. C2×#3675 | C22 | semidirect |
| 19. C4×C9⋊C8 | C22 | semidirect |
| 41. C2×C9⋊C8 | D4 | semidirect |
| 65. C2×C4×C9 | SD16 | semidirect |
| 73. C9⋊C8 | C2×D4 | semidirect |
| 75. C2×C4⋊Q8 | D9 | semidirect |
| 105. C4×C9 | C2×SD16 | semidirect |
| 114. C4⋊Q8 | C2×D9 | semidirect |
| 137. C2×C9 | #492 | semidirect |
| 169. C9 | C2×#492 | semidirect |
| 181. C2×C4 | #3675 | semidirect |
| 199. C4 | C2×#3675 | semidirect |
| 203. C2 | #10588770 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×C4⋊Q8 | 2 |
| C22×#3675 | 2 |
| C2×#63436 | 2 |
| #10588770 | 2 |
| C2×C4×C9⋊C8 | 2 |
| C2×#5085 | 3 |