Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
240 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 21. C4⋊#11715895 | C4 | semidirect |
| 22. #15690739 | C4 | semidirect |
| 23. #15690739 | C4 | semidirect |
| 24. C4⋊C8×C97 | C4 | semidirect |
| 111. C97 | #1949 | semidirect |
| 132. C4⋊C8 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690879 | 2 |
| C2×#15690878 | 2 |
| #20261679 | 2 |
| C4×C4⋊#87604 | 2 |
| #20261609 | 2 |
| C4⋊C8×D97 | 2 |
| #1949 | 97 |