Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
616 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 245 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×D4×Dic97 | C2 | semidirect |
| 2. D8×Dic97 | C2 | direct (N × H) |
| 3. C2×#15690744 | C2 | semidirect |
| 4. C2×#15690731 | C2 | semidirect |
| 5. C2×C8×Dic97 | C2 | semidirect |
| 10. D4×Dic97 | C22 | semidirect |
| 14. #15690744 | C22 | semidirect |
| 15. #15690731 | C22 | semidirect |
| 16. C8×Dic97 | C22 | semidirect |
| 18. C2×D8×C97 | C4 | semidirect |
| 36. C2×D4×C97 | C2×C4 | semidirect |
| 39. D8×C97 | C2×C4 | semidirect |
| 40. C2×C8×C97 | C2×C4 | semidirect |
| 49. D4×C97 | C22×C4 | semidirect |
| 58. C2×Dic97 | D8 | direct (N × H) |
| 61. C8×C97 | C22×C4 | semidirect |
| 76. Dic97 | C2×D8 | direct (N × H) |
| 78. C2×C97 | C4×D8 | semidirect |
| 83. C97 | C2×C4×D8 | semidirect |
| 92. C2×D8 | Dic97 | direct (N × H) |
| 107. C2×D4 | C2×Dic97 | semidirect |
| 115. D8 | C2×Dic97 | direct (N × H) |
| 118. C2×C8 | C2×Dic97 | semidirect |
| 132. D4 | C22×Dic97 | semidirect |
| 145. C8 | C22×Dic97 | semidirect |
| 161. C2 | D8×Dic97 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic97 | 2 |
| D8×Dic97 | 2 |
| C2×#15690744 | 2 |
| C2×#15690731 | 2 |
| C2×C8×Dic97 | 2 |
| C22×D8×C97 | 2 |
| C2×C4×D8 | 97 |