Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
170 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 47 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. #20261173 | C2 | semidirect |
| 2. #20261112 | C2 | semidirect |
| 3. #20260853 | C2 | semidirect |
| 4. #20260549 | C2 | semidirect |
| 5. #364×C97 | C2 | semidirect |
| 20. Dic388 | D4 | semidirect |
| 26. D776 | D4 | semidirect |
| 62. C97 | #2213 | semidirect |
| 66. #364 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261173 | 2 |
| #20261112 | 2 |
| #20260853 | 2 |
| #20260549 | 2 |
| #364×C97 | 2 |
| #2213 | 97 |