Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
924 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 237 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. C2×D4×Dic97 | C2 | semidirect |
| 3. C2×#15690772 | C2 | semidirect |
| 4. C2×#15690770 | C2 | semidirect |
| 5. #20260637 | C2 | semidirect |
| 6. #20260635 | C2 | semidirect |
| 7. #20260604 | C2 | semidirect |
| 8. C42×Dic97 | C2 | semidirect |
| 9. #390×C97 | C2 | semidirect |
| 14. #15690806 | C4 | semidirect |
| 34. C2×D388 | C2×C4 | semidirect |
| 37. C2×C22⋊D97 | C2×C4 | semidirect |
| 52. C4×Dic97 | C2×C4 | semidirect |
| 53. C4×Dic97 | D4 | semidirect |
| 54. C4×Dic97 | D4 | semidirect |
| 58. C2×D4×C97 | C2×C4 | semidirect |
| 115. C4×C97 | C4×D4 | semidirect |
| 118. Dic97 | C4×D4 | semidirect |
| 119. Dic97 | #127 | semidirect |
| 128. C97 | C4×#127 | semidirect |
| 135. #390 | D97 | semidirect |
| 169. C2×D4 | C4×D97 | semidirect |
| 247. C4 | #15690770 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690806 | 2 |
| C2×D4×Dic97 | 2 |
| C2×#15690772 | 2 |
| C2×#15690770 | 2 |
| #20260637 | 2 |
| #20260635 | 2 |
| #20260604 | 2 |
| C42×Dic97 | 2 |
| #390×C97 | 2 |
| C4×#127 | 97 |