Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
536 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 229 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. #20260776 | C2 | direct (N × H) |
| 5. C2×#15690743 | C2 | semidirect |
| 6. C2×#15690742 | C2 | semidirect |
| 7. C2×#15690741 | C2 | semidirect |
| 8. C2×#107×C97 | C2 | semidirect |
| 11. C2×#13095494 | C4 | semidirect |
| 23. #15690743 | C22 | semidirect |
| 24. #15690742 | C22 | semidirect |
| 25. #15690741 | C22 | semidirect |
| 29. #107×C97 | C22 | semidirect |
| 40. #13095494 | C2×C4 | semidirect |
| 41. C2×#11715895 | C2×C4 | semidirect |
| 53. C2×C8×C97 | C2×C4 | semidirect |
| 82. C8×C97 | C22×C4 | semidirect |
| 83. #11715895 | C22×C4 | semidirect |
| 100. C2×C97 | #428 | semidirect |
| 106. C97 | C2×#428 | semidirect |
| 112. C2×#107 | D97 | semidirect |
| 133. #107 | C2×D97 | semidirect |
| 152. C2×C8 | C4×D97 | semidirect |
| 189. C8 | C2×C4×D97 | semidirect |
| 207. C2 | #20260776 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095494 | 2 |
| C2×#15690768 | 2 |
| C2×C4⋊C4×D97 | 2 |
| #20260776 | 2 |
| C2×#15690743 | 2 |
| C2×#15690742 | 2 |
| C2×#15690741 | 2 |
| C2×#107×C97 | 2 |
| C2×#428 | 97 |