Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
354 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 21. C4×#157 | C8 | semidirect |
| 66. #157 | C4⋊C8 | semidirect |
| 68. C32×C4 | C4⋊C8 | semidirect |
| 71. C3⋊Dic3 | C4⋊C8 | semidirect |
| 128. C32 | #1842 | semidirect |
| 165. C4 | #63744 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×#157 | 2 |
| #10593726 | 2 |
| C2×#63744 | 2 |
| #1842 | 9 |