Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1018 conjugacy classes of subgroups; only the 338 normal subgroups are shown.
This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 338 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 |
|---|---|---|
| 4. C2×#63767 | C2 | direct (N × H) |
| 7. C22×#622 | C4 | semidirect |
| 10. C2×#3787 | C4 | semidirect |
| 12. C22×C32×C8 | C4 | semidirect |
| 13. C22×C3⋊(C3⋊C8) | C4 | semidirect |
| 14. C2×C8×C3⋊D3 | C4 | semidirect |
| 16. #63767 | C22 | direct (N × H) |
| 27. C2×#622 | C2×C4 | semidirect |
| 30. #3787 | C2×C4 | semidirect |
| 32. C2×C32×C8 | C2×C4 | semidirect |
| 33. C2×C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 34. C8×C3⋊D3 | C2×C4 | semidirect |
| 57. #622 | C22×C4 | semidirect |
| 58. C32×C8 | C22×C4 | semidirect |
| 59. C3⋊(C3⋊C8) | C22×C4 | semidirect |
| 75. C22×C32 | #97 | semidirect |
| 77. C2×C3⋊D3 | #97 | semidirect |
| 94. C22×C8 | #157 | semidirect |
| 113. C2×C32 | C2×#97 | semidirect |
| 115. C3⋊D3 | C2×#97 | semidirect |
| 132. C2×C8 | C2×#157 | semidirect |
| 145. C32 | C22×#97 | semidirect |
| 163. C8 | C22×#157 | semidirect |
| 172. C22 | #63767 | direct (N × H) |
| 182. C2 | C2×#63767 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#157 | 2 |
| C22×#3787 | 2 |
| C22×C8×C3⋊D3 | 2 |
| C2×#63767 | 2 |
| C22×#97 | 9 |