Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
456 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 177 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 |
|---|---|---|
| 2. C2×#15690818 | C2 | semidirect |
| 3. #20260856 | C2 | semidirect |
| 4. #20260851 | C2 | semidirect |
| 5. #20260751 | C2 | semidirect |
| 6. #20260693 | C2 | semidirect |
| 7. #430×C97 | C2 | semidirect |
| 9. #15690843 | C4 | semidirect |
| 10. #15690838 | C4 | semidirect |
| 14. #15690818 | C22 | semidirect |
| 15. #15690818 | C22 | semidirect |
| 20. #15690736 | C22 | semidirect |
| 21. #15690720 | C22 | semidirect |
| 22. C8×Dic97 | C22 | semidirect |
| 25. #108×C97 | C22 | semidirect |
| 90. C97 | #2955 | semidirect |
| 95. #430 | D97 | semidirect |
| 112. #108 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261535 | 2 |
| C2×#15690818 | 2 |
| #20260856 | 2 |
| #20260851 | 2 |
| #20260751 | 2 |
| #20260693 | 2 |
| #430×C97 | 2 |
| #2955 | 97 |