Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
272 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 272 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 |
|---|---|---|
| 1. C2×#15690905 | C2 | semidirect |
| 2. #20261832 | C2 | semidirect |
| 3. C22⋊#13095523 | C2 | semidirect |
| 6. C2×#13095523 | C22 | semidirect |
| 38. C22×D97 | C16 | semidirect |
| 60. C22×C97 | C2×C16 | semidirect |
| 67. C2×D97 | C2×C16 | semidirect |
| 79. D97 | C22⋊C16 | semidirect |
| 81. C97 | C2×C22⋊C16 | semidirect |
| 148. C22 | #15690905 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690905 | 2 |
| #20261832 | 2 |
| C22⋊#13095523 | 2 |
| C22×#13095519 | 2 |
| C2×C22⋊C16 | 97 |