Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
360 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 174 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 |
|---|---|---|
| 10. #15690865 | C4 | semidirect |
| 11. #15690864 | C4 | semidirect |
| 12. C8×#87604 | C4 | semidirect |
| 15. #15690721 | C4 | semidirect |
| 16. #15690720 | C4 | semidirect |
| 17. #97×C97 | C4 | semidirect |
| 47. #11715897 | C42 | semidirect |
| 48. C8×C97 | C42 | semidirect |
| 49. #11715895 | C42 | semidirect |
| 55. #87604 | #97 | direct (N × H) |
| 65. C97 | C4×#97 | semidirect |
| 81. #97 | #87604 | direct (N × H) |
| 114. C8 | C4×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20261694 | 2 |
| C2×#15690864 | 2 |
| C2×C8×#87604 | 2 |
| C42×#87604 | 2 |
| #97×D97 | 2 |
| C4×#97 | 97 |