Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1098 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 1098 conjugacy classes of subgroups — too many to draw. Only its 143 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×#64231 | C2 | semidirect |
| 2. C2×#64225 | C2 | semidirect |
| 3. C2×#63797 | C2 | semidirect |
| 4. C2×C8×#157 | C2 | semidirect |
| 5. #10593293 | C2 | direct (N × H) |
| 12. #64231 | C22 | semidirect |
| 14. #64225 | C22 | semidirect |
| 19. #63797 | C22 | semidirect |
| 20. C8×#157 | C22 | semidirect |
| 33. C2×#622 | D4 | semidirect |
| 36. #3787 | D4 | semidirect |
| 39. C2×C32×C8 | D4 | semidirect |
| 40. C2×C3⋊(C3⋊C8) | D4 | semidirect |
| 41. C8×C3⋊D3 | D4 | semidirect |
| 58. C2×#157 | D8 | semidirect |
| 71. #622 | C2×D4 | semidirect |
| 72. C32×C8 | C2×D4 | semidirect |
| 73. C3⋊(C3⋊C8) | C2×D4 | semidirect |
| 103. #157 | C2×D8 | semidirect |
| 143. C2×C32 | #493 | semidirect |
| 145. C3⋊D3 | #493 | semidirect |
| 168. C2×C8 | GO+(4,𝔽2) | semidirect |
| 185. C32 | C2×#493 | semidirect |
| 206. C8 | C2×GO+(4,𝔽2) | semidirect |
| 230. C2 | #10593293 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64231 | 2 |
| C2×#64225 | 2 |
| C2×#63797 | 2 |
| C2×C8×#157 | 2 |
| #10593293 | 2 |
| C2×#493 | 9 |