Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
232 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 64 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. #20261791 | C2 | semidirect |
| 2. C2×#15690878 | C2 | semidirect |
| 3. #20261652 | C2 | semidirect |
| 4. #20261651 | C2 | semidirect |
| 7. #15690885 | C22 | semidirect |
| 11. #15690878 | C22 | semidirect |
| 14. #15690832 | C4 | semidirect |
| 18. Q16×D97 | C4 | semidirect |
| 20. D8×D97 | C4 | semidirect |
| 22. #135×C97 | C4 | semidirect |
| 37. Dic388 | C2×C4 | semidirect |
| 42. D776 | C2×C4 | semidirect |
| 50. Q16×C97 | C2×C4 | semidirect |
| 52. D8×C97 | C2×C4 | semidirect |
| 102. D97 | #360 | semidirect |
| 104. C97 | C2×#360 | semidirect |
| 116. #135 | #87604 | semidirect |
| 141. Q16 | C2×#87604 | semidirect |
| 148. D8 | C2×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261791 | 2 |
| C2×#15690878 | 2 |
| #20261652 | 2 |
| #20261651 | 2 |
| #135×D97 | 2 |
| C2×#360 | 97 |