Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
280 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 114 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 |
|---|---|---|
| 9. C4×#11715895 | C4 | semidirect |
| 10. C8×Dic97 | C4 | semidirect |
| 11. C4×C8×C97 | C4 | semidirect |
| 35. C8×C97 | C4⋊C4 | semidirect |
| 36. #11715895 | C4⋊C4 | semidirect |
| 43. C4×C97 | #107 | semidirect |
| 45. Dic97 | #107 | semidirect |
| 53. C97 | #1845 | semidirect |
| 64. C4×C8 | #87604 | semidirect |
| 89. C8 | C4⋊#87604 | semidirect |
| 98. C4 | #15690879 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690879 | 2 |
| #20261681 | 2 |
| C4×C8×D97 | 2 |
| #1845 | 97 |