Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
360 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 125 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×Dic776 | C2 | semidirect |
| 3. C2×#15690756 | C2 | semidirect |
| 4. Q32×D97 | C2 | direct (N × H) |
| 6. C2×Q32×C97 | C2 | semidirect |
| 13. Dic776 | C22 | semidirect |
| 14. #15690756 | C22 | semidirect |
| 18. Q32×C97 | C22 | semidirect |
| 55. C2×D97 | Q32 | direct (N × H) |
| 62. C2×C97 | C2×Q32 | semidirect |
| 64. D97 | C2×Q32 | direct (N × H) |
| 66. C97 | C22×Q32 | semidirect |
| 71. C2×Q32 | D97 | direct (N × H) |
| 82. Q32 | C2×D97 | direct (N × H) |
| 129. C2 | Q32×D97 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D97 | 2 |
| C2×Dic776 | 2 |
| C2×#15690756 | 2 |
| Q32×D97 | 2 |
| C2×C16×D97 | 2 |
| C2×Q32×C97 | 2 |
| C22×Q32 | 97 |