Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
390 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 85 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. C2×M16×D97 | C2 | semidirect |
| 3. C2×#15690726 | C2 | semidirect |
| 4. C2×#15690726 | C2 | semidirect |
| 5. #20260698 | C2 | semidirect |
| 6. #20260504 | C2 | semidirect |
| 7. #343×C97 | C2 | semidirect |
| 52. #13095495 | D4 | semidirect |
| 64. M16×C97 | D4 | semidirect |
| 128. C2×D97 | #100 | semidirect |
| 145. C97 | #1900 | semidirect |
| 152. #343 | D97 | semidirect |
| 204. M16 | D388 | 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×#15690785 | 2 |
| C2×#15690726 | 2 |
| #20260698 | 2 |
| #20260504 | 2 |
| #343×C97 | 2 |
| #1900 | 97 |