Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
184 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20261838 | C2 | semidirect |
| 3. C4⋊#13095523 | C2 | semidirect |
| 37. C4×D97 | C16 | semidirect |
| 51. C4×C97 | C2×C16 | semidirect |
| 53. Dic97 | C2×C16 | semidirect |
| 59. D97 | C4⋊C16 | semidirect |
| 61. C97 | C2×C4⋊C16 | semidirect |
| 116. C4 | #15690905 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690905 | 2 |
| #20261838 | 2 |
| C4⋊#13095523 | 2 |
| C4×#13095519 | 2 |
| C2×C4⋊C16 | 97 |