Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
164 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 164 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 |
|---|---|---|
| 21. Q16×C97 | C8 | semidirect |
| 40. #11715895 | Q16 | direct (N × H) |
| 53. C97 | C8×Q16 | semidirect |
| 70. Q16 | #11715895 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#11715895 | 2 |
| #20260488 | 2 |
| Q8⋊#11715895 | 2 |
| C8×#11715895 | 2 |
| C4×Q16×C97 | 2 |
| C8×Q16 | 97 |