Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
648 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 152 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. #20261683 | C2 | semidirect |
| 2. #20261680 | C2 | semidirect |
| 8. #15690807 | C4 | semidirect |
| 9. #15690806 | C4 | semidirect |
| 11. #127×C97 | C4 | semidirect |
| 16. C2×D388 | C2×C4 | semidirect |
| 17. C2×C22⋊D97 | C2×C4 | semidirect |
| 21. C4×Dic97 | C2×C4 | semidirect |
| 22. C2×D4×C97 | C2×C4 | semidirect |
| 23. C42×C97 | C2×C4 | semidirect |
| 51. C97 | #2380 | semidirect |
| 59. #127 | #87604 | semidirect |
| 68. C2×D4 | C2×#87604 | semidirect |
| 74. C42 | C2×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261683 | 2 |
| #20261680 | 2 |
| #127×D97 | 2 |
| #2380 | 97 |