Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1434 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1434 conjugacy classes of subgroups — too many to draw. Only its 191 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. C32×#535 | C2 | semidirect |
| 2. C2×#64158 | C2 | semidirect |
| 3. C2×#64149 | C2 | semidirect |
| 4. C2×#63664 | C2 | semidirect |
| 5. C2×#63660 | C2 | semidirect |
| 6. #10592700 | C2 | semidirect |
| 7. #10589398 | C2 | semidirect |
| 30. C3×#535 | D3 | semidirect |
| 43. C2×C32×Q8 | D4 | semidirect |
| 52. C2×C32×D4 | D4 | semidirect |
| 63. C2×C4⋊(C3⋊D3) | D4 | semidirect |
| 64. C32×C4⋊C4 | D4 | semidirect |
| 71. C4×C3⋊Dic3 | D4 | semidirect |
| 75. #3748 | D4 | semidirect |
| 141. #535 | C3⋊D3 | semidirect |
| 153. C2×C3×Q8 | #67 | semidirect |
| 162. C2×C3×D4 | #67 | semidirect |
| 174. C3×C4⋊C4 | #67 | semidirect |
| 283. C2×Q8 | #638 | semidirect |
| 300. C2×D4 | #638 | semidirect |
| 312. C4⋊C4 | #638 | semidirect |
| 339. C32 | #2002 | semidirect |
| 408. C3 | #71856 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#535 | 2 |
| C2×#64158 | 2 |
| C2×#64149 | 2 |
| C2×#63664 | 2 |
| C2×#63660 | 2 |
| #10592700 | 2 |
| #10589398 | 2 |
| #71856 | 3 |