Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
310 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 66 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. #20261814 | C2 | semidirect |
| 2. #20261734 | C2 | semidirect |
| 3. #20261725 | C2 | semidirect |
| 4. #20261710 | C2 | semidirect |
| 5. #20261618 | C2 | semidirect |
| 6. #20261610 | C2 | semidirect |
| 25. #15690841 | C4 | semidirect |
| 26. #15690838 | C4 | semidirect |
| 28. #15690835 | C4 | semidirect |
| 32. #137×C97 | C4 | semidirect |
| 146. C97 | #1881 | semidirect |
| 158. #137 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261814 | 2 |
| #20261734 | 2 |
| #20261725 | 2 |
| #20261710 | 2 |
| #20261618 | 2 |
| #20261610 | 2 |
| #20261534 | 2 |
| #1881 | 97 |