Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 4. #20260693 | C2 | semidirect |
| 5. C2×#15690720 | C2 | semidirect |
| 6. #20260496 | C2 | semidirect |
| 7. #341×C97 | C2 | semidirect |
| 10. #15690818 | C4 | semidirect |
| 16. #15690736 | C4 | semidirect |
| 17. #15690735 | C4 | semidirect |
| 18. #15690732 | C4 | semidirect |
| 99. C97 | #1765 | semidirect |
| 105. #341 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690818 | 2 |
| C2×#15690736 | 2 |
| #20260732 | 2 |
| #20260693 | 2 |
| C2×#15690720 | 2 |
| #20260496 | 2 |
| #341×C97 | 2 |
| #1765 | 97 |