Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
266 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 70 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. #20261738 | C2 | semidirect |
| 2. C4×#13095520 | C2 | semidirect |
| 3. Q8⋊#11715897 | C2 | semidirect |
| 4. D4⋊#11715897 | C2 | semidirect |
| 55. Q8×C97 | M16 | semidirect |
| 58. D4×C97 | M16 | semidirect |
| 103. C97 | #1489 | semidirect |
| 158. Q8 | #13095520 | semidirect |
| 161. D4 | #13095520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261738 | 2 |
| C4×#13095520 | 2 |
| Q8⋊#11715897 | 2 |
| D4⋊#11715897 | 2 |
| #41×Dic97 | 2 |
| #1489 | 97 |