Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
777 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 777 conjugacy classes of subgroups — too many to draw. Only its 172 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×#63807 | C2 | semidirect |
| 2. C2×#63628 | C2 | semidirect |
| 3. C2×C3×D48 | C2 | semidirect |
| 4. C2×C3×D3×C16 | C2 | semidirect |
| 5. C2×#63548 | C2 | semidirect |
| 6. #10590241 | C2 | direct (N × H) |
| 15. #63807 | C22 | semidirect |
| 17. #63628 | C22 | semidirect |
| 19. C3×D48 | C22 | semidirect |
| 20. C3×D3×C16 | C22 | semidirect |
| 21. #63548 | C22 | semidirect |
| 33. C2×D48 | D3 | semidirect |
| 34. C2×D3×C16 | D3 | semidirect |
| 81. D48 | C2×D3 | semidirect |
| 82. D3×C16 | C2×D3 | semidirect |
| 206. C2×C32 | #508 | semidirect |
| 250. C32 | C2×#508 | semidirect |
| 271. C2×C3 | #4904 | semidirect |
| 272. C2×C3 | #4912 | semidirect |
| 287. C3 | C2×#4904 | semidirect |
| 288. C3 | C2×#4912 | semidirect |
| 291. C2 | #10590241 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63807 | 2 |
| C2×#63628 | 2 |
| C2×C3×D48 | 2 |
| C2×C3×D3×C16 | 2 |
| C2×#63548 | 2 |
| #10590241 | 2 |
| C2×#4912 | 3 |
| C2×#4904 | 3 |