Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
616 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 205 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×#15690772 | C2 | semidirect |
| 3. #20260817 | C2 | direct (N × H) |
| 4. C2×#15690730 | C2 | semidirect |
| 5. C2×C8×Dic97 | C2 | semidirect |
| 6. C2×#107×C97 | C2 | semidirect |
| 9. C2×D776 | C4 | semidirect |
| 13. #15690772 | C22 | semidirect |
| 16. #15690730 | C22 | semidirect |
| 17. C8×Dic97 | C22 | semidirect |
| 20. #107×C97 | C22 | semidirect |
| 24. C2×D388 | C2×C4 | semidirect |
| 30. D776 | C2×C4 | semidirect |
| 38. C2×C8×C97 | C2×C4 | semidirect |
| 54. C2×Dic97 | D8 | semidirect |
| 59. D388 | C22×C4 | semidirect |
| 61. C8×C97 | C22×C4 | semidirect |
| 76. Dic97 | C2×D8 | semidirect |
| 77. C2×C97 | C4×D8 | semidirect |
| 83. C97 | C2×C4×D8 | semidirect |
| 87. C2×#107 | D97 | semidirect |
| 101. #107 | C2×D97 | semidirect |
| 118. C2×C8 | C4×D97 | semidirect |
| 145. C8 | C2×C4×D97 | semidirect |
| 161. C2 | #20260817 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D776 | 2 |
| C2×#15690772 | 2 |
| #20260817 | 2 |
| C2×#15690730 | 2 |
| C2×C8×Dic97 | 2 |
| C2×#107×C97 | 2 |
| C2×C4×D8 | 97 |