Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1368 conjugacy classes of subgroups; only the 537 normal subgroups are shown.
This group has 1368 conjugacy classes of subgroups — too many to draw. Only its 537 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. #10592683 | C2 | semidirect |
| 3. #10592679 | C2 | semidirect |
| 6. #10592636 | C2 | semidirect |
| 7. #10592634 | C2 | semidirect |
| 10. C32×#126 | C4 | semidirect |
| 38. C32×C4⋊C4 | C2×C4 | semidirect |
| 40. C32×C42 | C2×C4 | semidirect |
| 48. C3×#126 | Dic3 | semidirect |
| 94. C3×C4⋊C4 | C2×Dic3 | semidirect |
| 96. C3×C42 | C2×Dic3 | semidirect |
| 115. #126 | C3⋊Dic3 | semidirect |
| 161. C4⋊C4 | C2×C3⋊Dic3 | semidirect |
| 165. C42 | C2×C3⋊Dic3 | semidirect |
| 178. C32 | #2383 | semidirect |
| 213. C3 | #83076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#126 | 2 |
| #10592683 | 2 |
| #10592679 | 2 |
| #10592650 | 2 |
| #10592649 | 2 |
| #10592636 | 2 |
| #10592634 | 2 |
| #83076 | 3 |