Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
348 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 104 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×#15690877 | C2 | semidirect |
| 3. C2×C4⋊#11715897 | C2 | semidirect |
| 5. #20261601 | C2 | semidirect |
| 6. #20261601 | C2 | semidirect |
| 49. #13095488 | C8 | semidirect |
| 73. C2×C4×C97 | C2×C8 | semidirect |
| 79. C2×Dic97 | C2×C8 | semidirect |
| 107. C2×D97 | C4⋊C8 | semidirect |
| 126. C97 | #1850 | semidirect |
| 215. C2×C4 | #13095519 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13095519 | 2 |
| C2×#15690877 | 2 |
| C2×C4⋊#11715897 | 2 |
| C2×#15690867 | 2 |
| #20261601 | 2 |
| #20260582 | 2 |
| #1850 | 97 |