Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
152 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 64 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 |
|---|---|---|
| 2. #20261662 | C2 | semidirect |
| 3. #20261661 | C2 | semidirect |
| 9. C2×#13095486 | C4 | semidirect |
| 10. C16×D97 | C4 | semidirect |
| 11. C16×D97 | C4 | semidirect |
| 14. C2×C16×C97 | C4 | semidirect |
| 55. C97 | #2158 | semidirect |
| 67. C2×C16 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261745 | 2 |
| #20261662 | 2 |
| #20261661 | 2 |
| C2×C16×D97 | 2 |
| #2158 | 97 |