Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #20261363 | C2 | semidirect |
| 3. #20261100 | C2 | semidirect |
| 4. #20261095 | C2 | semidirect |
| 5. #20261090 | C2 | semidirect |
| 6. #20261082 | C2 | semidirect |
| 7. #20260741 | C2 | semidirect |
| 8. #20260737 | C2 | semidirect |
| 9. #20260732 | C2 | semidirect |
| 10. C2×#15690732 | C2 | semidirect |
| 11. #405×C97 | C2 | semidirect |
| 14. #15690810 | C22 | semidirect |
| 17. #15690802 | C22 | semidirect |
| 26. #15690735 | C22 | semidirect |
| 27. #15690735 | C22 | semidirect |
| 28. #15690735 | C22 | semidirect |
| 33. #15690732 | C22 | semidirect |
| 34. #15690732 | C22 | semidirect |
| 35. #15690732 | C22 | semidirect |
| 39. #97×C97 | C22 | semidirect |
| 40. C4×C8×C97 | C22 | semidirect |
| 136. C97 | #3136 | semidirect |
| 147. #405 | D97 | semidirect |
| 175. #97 | C2×D97 | semidirect |
| 176. C4×C8 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261363 | 2 |
| #20261304 | 2 |
| #20261100 | 2 |
| #20261095 | 2 |
| #20261090 | 2 |
| #20261082 | 2 |
| #20260741 | 2 |
| #20260737 | 2 |
| #20260732 | 2 |
| C2×#15690732 | 2 |
| #405×C97 | 2 |
| #3136 | 97 |