Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
840 conjugacy classes of subgroups; only the 338 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 338 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. #20261671 | C2 | direct (N × H) |
| 6. C2×C4×#87604 | C4 | semidirect |
| 11. C2×C4×Dic97 | C4 | semidirect |
| 12. C2×C4×Dic97 | C4 | semidirect |
| 13. C42×D97 | C4 | semidirect |
| 15. C2×C42×C97 | C4 | semidirect |
| 19. C4×#87604 | C2×C4 | semidirect |
| 29. C4×Dic97 | C2×C4 | semidirect |
| 30. C4×Dic97 | C2×C4 | semidirect |
| 33. C42×C97 | C2×C4 | semidirect |
| 67. C2×C97 | #376 | semidirect |
| 70. D97 | #376 | semidirect |
| 73. C97 | C2×#376 | semidirect |
| 87. C2×C42 | #87604 | semidirect |
| 106. C42 | C2×#87604 | semidirect |
| 142. C2 | #20261671 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×#87604 | 2 |
| #20261671 | 2 |
| C2×(C2×#87604)⋊C4 | 2 |
| C2×C42×D97 | 2 |
| C2×#376 | 97 |