Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
398 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 166 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. #20261786 | C2 | semidirect |
| 2. #20261766 | C2 | semidirect |
| 3. D4×#11715897 | C2 | semidirect |
| 4. #20261755 | C2 | semidirect |
| 5. #20261752 | C2 | semidirect |
| 6. #20261738 | C2 | semidirect |
| 7. C2×#15690877 | C2 | semidirect |
| 64. D4×C97 | M16 | semidirect |
| 108. C97 | #2990 | semidirect |
| 172. D4 | #13095520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261786 | 2 |
| #20261766 | 2 |
| D4×#11715897 | 2 |
| #20261755 | 2 |
| #20261752 | 2 |
| #20261738 | 2 |
| C2×#15690877 | 2 |
| #41×Dic97 | 2 |
| #2990 | 97 |