Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
496 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 135 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. C2×#15690840 | C2 | semidirect |
| 2. C2×M16×D97 | C2 | semidirect |
| 4. C2×#15690790 | C2 | semidirect |
| 5. #20260992 | C2 | semidirect |
| 6. #20260980 | C2 | semidirect |
| 7. #20260975 | C2 | semidirect |
| 8. #20260963 | C2 | semidirect |
| 9. #20260775 | C2 | semidirect |
| 10. #20260745 | C2 | semidirect |
| 11. #417×C97 | C2 | semidirect |
| 15. C2×#13095501 | C22 | semidirect |
| 16. C2×#13095499 | C22 | semidirect |
| 36. #15690743 | C22 | semidirect |
| 37. #15690741 | C22 | semidirect |
| 38. #15690735 | C22 | semidirect |
| 39. #15690735 | C22 | semidirect |
| 43. #103×C97 | C22 | semidirect |
| 44. #102×C97 | C22 | semidirect |
| 62. #13095495 | D4 | semidirect |
| 145. C2×D97 | #137 | semidirect |
| 164. C97 | #3056 | semidirect |
| 175. #417 | D97 | semidirect |
| 207. #103 | C2×D97 | semidirect |
| 208. #102 | C2×D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690840 | 2 |
| C2×M16×D97 | 2 |
| #20261242 | 2 |
| C2×#15690790 | 2 |
| #20260992 | 2 |
| #20260980 | 2 |
| #20260975 | 2 |
| #20260963 | 2 |
| #20260775 | 2 |
| #20260745 | 2 |
| #417×C97 | 2 |
| #3056 | 97 |