Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
136 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 52 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 |
|---|---|---|
| 7. #15690880 | C4 | semidirect |
| 13. C2×#13095486 | C4 | semidirect |
| 14. C2×C16×C97 | C4 | semidirect |
| 61. C97 | #1383 | semidirect |
| 71. C2×C16 | #87604 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690880 | 2 |
| C2×#15690878 | 2 |
| C2×#15690749 | 2 |
| #1383 | 97 |