Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
574 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 154 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 |
|---|---|---|
| 13. #63779 | C4 | direct (N × H) |
| 29. C4×C3⋊Dic3 | C8 | semidirect |
| 30. C4×C3⋊Dic3 | C8 | semidirect |
| 94. C32×C4 | C4⋊C8 | semidirect |
| 96. C3⋊Dic3 | C4×C8 | semidirect |
| 97. C3⋊Dic3 | C4⋊C8 | semidirect |
| 173. C32 | C4×C4⋊C8 | semidirect |
| 219. C4 | #63779 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63779 | 2 |
| C2×C4×#622 | 2 |
| C42×C3⋊Dic3 | 2 |
| #10590207 | 2 |
| C4×C4⋊C8 | 9 |