Finite Group DatabasebetaFinite Group DatabasebetaOrder 12416.
396 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 157 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. C4×C4⋊Dic97 | C2 | semidirect |
| 4. #20260497 | C2 | semidirect |
| 9. #15690731 | C4 | direct (N × H) |
| 15. C4×D4×C97 | C4 | semidirect |
| 22. C2×#11715895 | C2×C4 | semidirect |
| 24. C4⋊Dic97 | C2×C4 | semidirect |
| 51. D4×C97 | C42 | semidirect |
| 81. C4×C97 | #102 | semidirect |
| 93. C97 | C4×#102 | semidirect |
| 103. C4×D4 | Dic97 | semidirect |
| 144. D4 | C4×Dic97 | semidirect |
| 175. C4 | #15690731 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690731 | 2 |
| C2×C4×#11715895 | 2 |
| C4×C4⋊Dic97 | 2 |
| #20260497 | 2 |
| C2×C4×D4×C97 | 2 |
| C4×#102 | 97 |