Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1110 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 1110 conjugacy classes of subgroups — too many to draw. Only its 253 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 |
|---|---|---|
| 69. C2×C32×C4 | Q16 | semidirect |
| 142. C2×C3×C4 | #216 | semidirect |
| 193. C32 | #2016 | semidirect |
| 211. C2×C4 | #3756 | semidirect |
| 233. C3 | #69691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#3756 | 2 |
| C2×#64078 | 2 |
| C32×#391 | 2 |
| C2×#63637 | 2 |
| #10589390 | 2 |
| #69691 | 3 |