Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2793 conjugacy classes of subgroups; only the 490 normal subgroups are shown.
This group has 2793 conjugacy classes of subgroups — too many to draw. Only its 490 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×C32×#127 | C2 | semidirect |
| 2. C2×C3×#940 | C2 | semidirect |
| 3. C2×C3×#874 | C2 | semidirect |
| 4. C3×C42×Dic3 | C2 | semidirect |
| 6. #83185 | C3 | direct (N × H) |
| 18. C2×C3×#127 | D3 | semidirect |
| 19. C2×C3×#127 | C2×C3 | semidirect |
| 20. C2×#940 | C2×C3 | semidirect |
| 21. C2×#874 | C2×C3 | semidirect |
| 23. C42×Dic3 | C2×C3 | semidirect |
| 33. C32×C42 | D4 | semidirect |
| 34. C3×C4×Dic3 | D4 | semidirect |
| 68. C2×#127 | C3×D3 | semidirect |
| 94. C3×C42 | #67 | semidirect |
| 95. C3×C42 | C3×D4 | semidirect |
| 96. C4×Dic3 | C3×D4 | semidirect |
| 103. C32×C4 | #127 | semidirect |
| 104. C3×Dic3 | #127 | semidirect |
| 155. C42 | C3×#67 | semidirect |
| 174. C3×C4 | #940 | semidirect |
| 175. C3×C4 | C3×#127 | semidirect |
| 176. Dic3 | C3×#127 | semidirect |
| 177. C32 | #2867 | semidirect |
| 207. C4 | C3×#940 | semidirect |
| 209. C3 | #83185 | direct (N × H) |
| 210. C3 | C3×#2867 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#127 | 2 |
| C2×C3×#940 | 2 |
| C2×C3×#874 | 2 |
| C3×C42×Dic3 | 2 |
| C3×#2867 | 3 |
| #83185 | 3 |