Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1049 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 1049 conjugacy classes of subgroups — too many to draw. Only its 212 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×#63872 | C2 | semidirect |
| 3. C2×#63642 | C2 | semidirect |
| 4. C2×C3×#821 | C2 | semidirect |
| 5. C2×#63562 | C2 | semidirect |
| 6. #10590888 | C2 | direct (N × H) |
| 18. #63872 | C22 | semidirect |
| 19. #63642 | C22 | semidirect |
| 20. C3×#821 | C22 | semidirect |
| 21. #63562 | C22 | semidirect |
| 26. C2×#821 | D3 | semidirect |
| 71. #821 | C2×D3 | semidirect |
| 205. C2×C32 | #490 | semidirect |
| 254. C32 | C2×#490 | semidirect |
| 278. C2×C3 | #4764 | semidirect |
| 296. C3 | C2×#4764 | semidirect |
| 298. C2 | #10590888 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63914 | 2 |
| C2×#63872 | 2 |
| C2×#63642 | 2 |
| C2×C3×#821 | 2 |
| C2×#63562 | 2 |
| #10590888 | 2 |
| C2×#4764 | 3 |