Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
280 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 280 conjugacy classes of subgroups — too many to draw. Only its 106 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. #15690878 | C4 | semidirect |
| 11. C8×#87604 | C4 | semidirect |
| 15. #15690742 | C4 | semidirect |
| 16. #15690741 | C4 | semidirect |
| 17. #106×C97 | C4 | semidirect |
| 57. C8×C97 | C42 | semidirect |
| 58. #11715895 | C42 | semidirect |
| 66. #87604 | #106 | direct (N × H) |
| 79. C97 | C4×#106 | semidirect |
| 94. #106 | #87604 | direct (N × H) |
| 137. C8 | C4×#87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690878 | 2 |
| C2×C8×#87604 | 2 |
| C4⋊C4×#87604 | 2 |
| #20261608 | 2 |
| #106×D97 | 2 |
| C4×#106 | 97 |