Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
346 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 144 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. #20261786 | C2 | semidirect |
| 2. #20261768 | C2 | semidirect |
| 3. #20261766 | C2 | semidirect |
| 4. #20261764 | C2 | semidirect |
| 5. #20261759 | C2 | semidirect |
| 6. #20261757 | C2 | semidirect |
| 7. #20261741 | C2 | semidirect |
| 8. #20261740 | C2 | semidirect |
| 115. C97 | #2995 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261786 | 2 |
| #20261768 | 2 |
| #20261766 | 2 |
| #20261764 | 2 |
| #20261759 | 2 |
| #20261757 | 2 |
| #20261741 | 2 |
| #20261740 | 2 |
| #20261264 | 2 |
| #2995 | 97 |