Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
172 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 61 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. #20261115 | C2 | semidirect |
| 3. #20260488 | C2 | semidirect |
| 4. #20260482 | C2 | semidirect |
| 34. D4×C97 | Q16 | semidirect |
| 64. C97 | #1669 | semidirect |
| 100. D4 | Dic388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261115 | 2 |
| #20261015 | 2 |
| #20260488 | 2 |
| #20260482 | 2 |
| C8×D4×C97 | 2 |
| #1669 | 97 |