Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1249 conjugacy classes of subgroups; only the 188 normal subgroups are shown.
This group has 1249 conjugacy classes of subgroups — too many to draw. Only its 188 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. C2×C3×#830 | C2 | semidirect |
| 3. #10589146 | C2 | direct (N × H) |
| 14. C3×#830 | C22 | semidirect |
| 18. C2×#830 | D3 | semidirect |
| 26. C23×C3⋊D3 | C8 | semidirect |
| 63. #830 | C2×D3 | semidirect |
| 83. C22×C3⋊D3 | C2×C8 | semidirect |
| 246. C2×C32 | #323 | semidirect |
| 320. C32 | C2×#323 | semidirect |
| 362. C2×C3 | #4468 | semidirect |
| 392. C3 | C2×#4468 | semidirect |
| 397. C2 | #10589146 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3752 | 2 |
| C2×C3×#830 | 2 |
| #10589146 | 2 |
| C2×#4468 | 3 |