Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
220 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 62 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. #20261791 | C2 | semidirect |
| 2. C2×#15690881 | C2 | semidirect |
| 3. #20261650 | C2 | semidirect |
| 4. #20261649 | C2 | semidirect |
| 9. #15690883 | C22 | semidirect |
| 11. #15690881 | C22 | semidirect |
| 102. C97 | #2143 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261791 | 2 |
| C2×#15690881 | 2 |
| #20261650 | 2 |
| #20261649 | 2 |
| #135×D97 | 2 |
| #2143 | 97 |