Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
648 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 117 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. C32×#473 | C2 | semidirect |
| 3. #10592878 | C2 | semidirect |
| 4. C2×#63655 | C2 | semidirect |
| 5. #10589427 | C2 | semidirect |
| 6. #10589363 | C2 | semidirect |
| 7. #10589361 | C2 | semidirect |
| 11. C2×C32×Q16 | C22 | semidirect |
| 19. C32×#108 | C22 | semidirect |
| 24. #63639 | C22 | semidirect |
| 25. C2×C3⋊(C3⋊C16) | C22 | semidirect |
| 27. C3×#473 | D3 | semidirect |
| 63. C2×C3×Q16 | C2×D3 | semidirect |
| 71. C3×#108 | C2×D3 | semidirect |
| 104. #473 | C3⋊D3 | semidirect |
| 152. C2×Q16 | C2×C3⋊D3 | semidirect |
| 161. #108 | C2×C3⋊D3 | semidirect |
| 229. C32 | #2194 | semidirect |
| 269. C3 | #71098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596223 | 2 |
| C32×#473 | 2 |
| #10592878 | 2 |
| C2×#63655 | 2 |
| #10589427 | 2 |
| #10589363 | 2 |
| #10589361 | 2 |
| #71098 | 3 |