Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
432 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 432 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. C23×#11715906 | C2 | semidirect |
| 2. C2×C22⋊#11715906 | C2 | semidirect |
| 3. C2×C22⋊#11715906 | C2 | semidirect |
| 4. (C2×#11715906)⋊C4 | C2 | semidirect |
| 27. C2×#11715906 | D4 | semidirect |
| 47. C2×D388 | C8 | semidirect |
| 48. C2×C22⋊D97 | C8 | semidirect |
| 49. C2×C22⋊D97 | C8 | semidirect |
| 53. C2×D4×C97 | C8 | semidirect |
| 55. C23×C97 | C2×C8 | semidirect |
| 64. C22×D97 | C2×C8 | semidirect |
| 86. C2×C4×C97 | C2×C8 | semidirect |
| 89. C2×Dic97 | C2×C8 | semidirect |
| 96. C22×C97 | C22⋊C8 | semidirect |
| 107. C2×D97 | C22⋊C8 | semidirect |
| 130. C97 | #1869 | semidirect |
| 158. C2×D4 | #11715906 | semidirect |
| 196. C23 | C2×#11715906 | semidirect |
| 220. C2×C4 | C2×#11715906 | semidirect |
| 240. C22 | C22⋊#11715906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11715906 | 2 |
| C2×C22⋊#11715906 | 2 |
| (C2×#11715906)⋊C4 | 2 |
| C2×D4×#87604 | 2 |
| #1869 | 97 |