Finite Group DatabasebetaFinite Group DatabasebetaOrder 12288.
At least 10119 conjugacy classes of subgroups; only the 30 normal subgroups are shown.
This group has at least 10119 conjugacy classes of subgroups — too many to draw. Only its 30 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. #72252402 | C3 | semidirect |
| 2. #72241400 | C2 | semidirect |
| 3. #72241399 | C2×C3 | semidirect |
| 4. #72241390 | C2 | semidirect |
| 5. #72241389 | C2×C3 | semidirect |
| 6. #72227620 | C2 | semidirect |
| 7. #72227590 | C2×C3 | semidirect |
| 9. #72227582 | D4 | semidirect |
| 11. #72210025 | A4 | semidirect |
| 12. H(9,𝔽2) | C2×A4 | semidirect |
| 13. #8934620 | C3×D4 | semidirect |
| 15. #392135 | C2×A4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #72252402 | 3 |
| #72252401 | 4 |
| #72241400 | 2 |
| #72241390 | 2 |
| #72227620 | 2 |