Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
520 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 2. #20260639 | C2 | semidirect |
| 3. #20260629 | C2 | semidirect |
| 4. #20260623 | C2 | semidirect |
| 6. #20260608 | C2 | semidirect |
| 7. #20260607 | C2 | semidirect |
| 8. #20260599 | C2 | semidirect |
| 12. #15690797 | C4 | semidirect |
| 34. C2×Dic194 | C2×C4 | semidirect |
| 46. C22⋊Dic97 | C2×C4 | semidirect |
| 47. C22⋊Dic97 | C2×C4 | semidirect |
| 49. C4×Dic97 | C2×C4 | semidirect |
| 128. C97 | #2379 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690797 | 2 |
| #20260639 | 2 |
| #20260629 | 2 |
| #20260623 | 2 |
| #20260615 | 2 |
| #20260608 | 2 |
| #20260607 | 2 |
| #20260599 | 2 |
| #386×C97 | 2 |
| #2379 | 97 |