Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
172 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 53 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. #20261114 | C2 | semidirect |
| 5. #20260487 | C2 | semidirect |
| 6. #20260482 | C2 | semidirect |
| 7. #332×C97 | C2 | semidirect |
| 52. D388 | Q16 | semidirect |
| 79. C97 | #1669 | semidirect |
| 86. #332 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261114 | 2 |
| #20261016 | 2 |
| #20261012 | 2 |
| #20260800 | 2 |
| #20260487 | 2 |
| #20260482 | 2 |
| #332×C97 | 2 |
| #1669 | 97 |