Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
478 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 135 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 |
|---|---|---|
| 11. #63732 | C4 | direct (N × H) |
| 22. C4×#157 | C8 | semidirect |
| 73. #157 | C4×C8 | semidirect |
| 74. C32×C4 | C4⋊C8 | semidirect |
| 76. C3⋊Dic3 | C4⋊C8 | semidirect |
| 127. C32 | C4×C4⋊C8 | semidirect |
| 160. C4 | #63732 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×#157 | 2 |
| C2×#63732 | 2 |
| C4×#3710 | 2 |
| #10590044 | 2 |
| C4×C4⋊C8 | 9 |