Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
456 conjugacy classes of subgroups; only the 212 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 212 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. Q8×#11715897 | C2 | semidirect |
| 2. #20261763 | C2 | semidirect |
| 3. #20261754 | C2 | semidirect |
| 4. C4×#13095519 | C2 | semidirect |
| 22. #13095512 | C8 | semidirect |
| 36. Q8×C97 | C2×C8 | semidirect |
| 43. D388 | C2×C8 | semidirect |
| 46. C4×D97 | C2×C8 | semidirect |
| 48. #11715897 | #41 | semidirect |
| 64. C97 | C8×#41 | semidirect |
| 100. Q8 | #13095519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11715897 | 2 |
| #20261763 | 2 |
| #20261754 | 2 |
| C4×#13095519 | 2 |
| C4×#13095512 | 2 |
| C8×#41 | 97 |