Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2280 conjugacy classes of subgroups; only the 313 normal subgroups are shown.
This group has 2280 conjugacy classes of subgroups — too many to draw. Only its 313 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×#64145 | C2 | semidirect |
| 3. C2×#64118 | C2 | semidirect |
| 4. C2×C32×#100 | C2 | semidirect |
| 5. C2×#63652 | C2 | semidirect |
| 6. #10592445 | C2 | direct (N × H) |
| 16. C22×#634 | C22 | semidirect |
| 17. C2×C32×M16 | C22 | semidirect |
| 20. #64145 | C22 | semidirect |
| 21. C2×C4×C3⋊Dic3 | C22 | semidirect |
| 23. #64118 | C22 | semidirect |
| 26. C32×#100 | C22 | semidirect |
| 27. #63652 | C22 | semidirect |
| 31. C2×C3×#100 | D3 | semidirect |
| 62. C2×#634 | C23 | semidirect |
| 64. C32×M16 | C23 | semidirect |
| 68. C4×C3⋊Dic3 | C23 | semidirect |
| 81. C2×C3×M16 | C2×D3 | semidirect |
| 90. C3×#100 | C2×D3 | semidirect |
| 130. C2×#100 | C3⋊D3 | semidirect |
| 161. C3×M16 | C22×D3 | semidirect |
| 197. C2×M16 | C2×C3⋊D3 | semidirect |
| 203. #100 | C2×C3⋊D3 | semidirect |
| 240. C2×C32 | #455 | semidirect |
| 275. M16 | C22×C3⋊D3 | semidirect |
| 296. C32 | C2×#455 | semidirect |
| 333. C2×C3 | #4746 | semidirect |
| 352. C3 | C2×#4746 | semidirect |
| 357. C2 | #10592445 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64361 | 2 |
| C2×#64145 | 2 |
| C2×#64118 | 2 |
| C2×C32×#100 | 2 |
| C2×#63652 | 2 |
| #10592445 | 2 |
| C2×#4746 | 3 |