Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
384 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 2. C2×C4⋊#11715895 | C2 | semidirect |
| 3. C2×#15690722 | C2 | semidirect |
| 4. C2×#97×C97 | C2 | semidirect |
| 34. C2×C8×C97 | D4 | semidirect |
| 80. C97 | #1955 | semidirect |
| 84. C2×#97 | D97 | semidirect |
| 112. C2×C8 | D388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D388 | 2 |
| C2×C4⋊#11715895 | 2 |
| C2×#15690722 | 2 |
| C2×#97×C97 | 2 |
| #1955 | 97 |