Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
144 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 43 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. C2×#15690754 | C2 | semidirect |
| 2. #20261153 | C2 | semidirect |
| 3. #20261011 | C2 | semidirect |
| 5. #20260564 | C2 | semidirect |
| 6. #20260552 | C2 | semidirect |
| 7. #361×C97 | C2 | semidirect |
| 72. C97 | #2223 | semidirect |
| 79. #361 | D97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690754 | 2 |
| #20261153 | 2 |
| #20261011 | 2 |
| #20261002 | 2 |
| #20260564 | 2 |
| #20260552 | 2 |
| #361×C97 | 2 |
| #2223 | 97 |