Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
396 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 1. C2×C4⋊#11715906 | C2 | semidirect |
| 2. C2×C22⋊#11715906 | C2 | semidirect |
| 3. C2×C4×#11715906 | C2 | semidirect |
| 21. C2×#11715906 | D4 | semidirect |
| 34. C2×D388 | C8 | semidirect |
| 35. C2×C22⋊D97 | C8 | semidirect |
| 39. C2×D4×C97 | C8 | semidirect |
| 84. C4×C97 | C22⋊C8 | semidirect |
| 85. Dic97 | C22⋊C8 | semidirect |
| 94. C97 | #1954 | semidirect |
| 116. C2×D4 | #11715906 | semidirect |
| 179. C4 | C22⋊#11715906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊#11715906 | 2 |
| C2×C22⋊#11715906 | 2 |
| C2×C4×#11715906 | 2 |
| C2×D4×#87604 | 2 |
| #1954 | 97 |