Finite Group DatabasebetaFinite Group DatabasebetaOrder 1536.
264 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 1. #10715756 | C2 | semidirect |
| 2. #10682855 | C2 | semidirect |
| 3. #10682634 | C2 | semidirect |
| 4. #10682520 | C2 | semidirect |
| 173. C3 | #151103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10715756 | 2 |
| #10682855 | 2 |
| #10682634 | 2 |
| #10682520 | 2 |
| C3×#12047 | 2 |
| #151103 | 3 |