Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
368 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 368 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. C2×#15690832 | C2 | semidirect |
| 2. #20261165 | C2 | direct (N × H) |
| 3. C2×#15690756 | C2 | semidirect |
| 4. C2×#15690754 | C2 | semidirect |
| 5. C2×#15690753 | C2 | semidirect |
| 6. C2×#15690751 | C2 | semidirect |
| 7. C22×#13095486 | C2 | semidirect |
| 8. C2×#135×C97 | C2 | semidirect |
| 11. #15690832 | C22 | semidirect |
| 15. #15690756 | C22 | semidirect |
| 16. #15690754 | C22 | semidirect |
| 17. #15690753 | C22 | semidirect |
| 18. #15690751 | C22 | semidirect |
| 21. C2×#13095486 | C22 | semidirect |
| 24. #135×C97 | C22 | semidirect |
| 96. C2×C97 | #508 | semidirect |
| 100. C97 | C2×#508 | semidirect |
| 102. C2×#135 | D97 | semidirect |
| 114. #135 | C2×D97 | semidirect |
| 197. C2 | #20261165 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690832 | 2 |
| #20261165 | 2 |
| C2×#15690756 | 2 |
| C2×#15690754 | 2 |
| C2×#15690753 | 2 |
| C2×#15690751 | 2 |
| C22×#13095486 | 2 |
| C2×#135×C97 | 2 |
| C2×#508 | 97 |