Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
348 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 129 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 |
|---|---|---|
| 3. C2×#15690720 | C2 | semidirect |
| 4. C2×C4×#11715895 | C2 | semidirect |
| 6. #20260489 | C2 | semidirect |
| 7. #336×C97 | C2 | semidirect |
| 11. C2×#13095494 | C4 | semidirect |
| 16. #15690722 | C4 | semidirect |
| 60. C2×C4×C97 | M16 | semidirect |
| 80. #11715895 | C22⋊C4 | semidirect |
| 105. C97 | #1753 | semidirect |
| 112. #336 | D97 | semidirect |
| 175. C2×C4 | #13095494 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095494 | 2 |
| C2×#15690722 | 2 |
| C2×#15690720 | 2 |
| C2×C4×#11715895 | 2 |
| C4×#13095488 | 2 |
| #20260489 | 2 |
| #336×C97 | 2 |
| #1753 | 97 |