Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
388 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 137 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. #20260504 | C2 | semidirect |
| 4. #20260503 | C2 | semidirect |
| 5. #343×C97 | C2 | semidirect |
| 10. M16×D97 | C4 | semidirect |
| 89. C97 | #1742 | semidirect |
| 94. #343 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×D97 | 2 |
| C2×#15690768 | 2 |
| #20260504 | 2 |
| #20260503 | 2 |
| #343×C97 | 2 |
| #1742 | 97 |