Finite Group DatabasebetaFinite Group DatabasebetaOrder 1536.
264 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 95 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. #10715755 | C2 | semidirect |
| 3. #10682633 | C2 | semidirect |
| 4. #10682520 | C2 | semidirect |
| 5. C3×#7456 | C2 | semidirect |
| 19. #7456 | D3 | semidirect |
| 173. C3 | #151103 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10715755 | 2 |
| #10706949 | 2 |
| #10682633 | 2 |
| #10682520 | 2 |
| C3×#7456 | 2 |
| #151103 | 3 |