Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
432 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
| 11. M16×D97 | C4 | semidirect |
| 31. #13095495 | C2×C4 | semidirect |
| 40. M16×C97 | C2×C4 | semidirect |
| 93. D97 | #343 | direct (N × H) |
| 95. C97 | C2×#343 | semidirect |
| 100. #343 | D97 | direct (N × H) |
| 131. M16 | C4×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×C4⋊C4×D97 | 2 |
| #20260504 | 2 |
| #20260503 | 2 |
| #343×C97 | 2 |
| C2×#343 | 97 |